# User talk:Sławomir Biały

(Redirected from User talk:Slawekb)

I laughed out loud reading your post about reverting the code inserted into the prime numbers article.... I fell out of my chair when I actually saw the code.... The fact that the guy wanted to solve the Goldbach conjecture with that... RockvilleRideOn (talk) 03:48, 4 February 2013 (UTC)

I saw your talk on 'Fourier transform'. If you have time, could you just explain a little more on normalization problem? Or state in the page so reader could be aware of this. Thanks. Allenleeshining (talk) 17:34, 4 January 2013 (UTC) http://en.wikipedia.org/wiki/Talk:Fourier_transform#Suspect_wrong_equations_in_section_.27Square-integrable_functions.27

## Does fixing some trivial math typos require commenting?

Hi Sławo, I fixed some math formatting in the Taylor's series section, which you have reverted to the original. I didn't realize I had to justify this as the changes were obviously typographical from the diff output. cerniagigante (talk) 01:09, 1 March 2016 (UTC)

Why should one small section of the article be changed to a notation and styling that is inconsistent with the rest of the article? That's what needs to be justified. Also WP:MSM cautions against large-scale stylistic changes from inline html to LaTeX, or vice versa. 01:38, 1 March 2016 (UTC)

## Taylor Series Exemple

Hi Sławomir Biały. Following your correction. How can you explain the following identity:

{\displaystyle {\begin{aligned}\sum _{n=0}^{\infty }{x^{n+1} \over n!}=\sum _{n=1}^{\infty }{x^{n} \over (n-1)!}\end{aligned}}}

My calculus will be

{\displaystyle {\begin{aligned}\sum _{n=0}^{\infty }{x^{n+1} \over n!}=x+\sum _{n=1}^{\infty }{x^{n+1} \over n!}=x+x\sum _{n=1}^{\infty }{x^{n} \over n!}\end{aligned}}} and not the initial result.

This way I get to the final result of {\displaystyle {\begin{aligned}\sum _{n=0}^{\infty }{x^{n}(x+1) \over n!}\end{aligned}}} instead of {\displaystyle {\begin{aligned}\sum _{n=0}^{\infty }{x^{n}(n+1) \over n!}\end{aligned}}}

Please correct me if I'm wrong — Preceding unsigned comment added by Lupflamind (talkcontribs) 15:10, 6 February 2014 (UTC)

These series are equal to each other. So what you have is correct, but it isn't a Taylor series since it's not a power series. Sławomir Biały (talk) 15:34, 6 February 2014 (UTC)

## Response:Topologies of uniform convergence

Hi Sławomir Biały. It's fine if you want to change the name however I would not pick the name "Uniform convergence in a topological vector space" since there is after all a concept in general topology about uniform convergence (i.e. uniformities) that in particular applies to all TVSs. Maybe change it to "Topologies of Uniform Convergence on Vector Spaces of Maps"? Also, I do have a very general introduction but that's because otherwise the same concepts would have to continuously reappear throughout the subsection. Mgkrupa (talk) 16:13, 26 January 2014 (UTC)

Left response on my talk page (did it automatically notify you of this?).Mgkrupa (talk) 00:37, 27 January 2014 (UTC)

## Talkback

Hello, Sławomir Biały. You have new messages at 2001:db8's talk page.
Message added 23:27, 11 February 2013 (UTC). You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

– 2001:db8:: (rfc | diff) 23:27, 11 February 2013 (UTC)

## Talkback

I responded to your question at the Math reference desk at Wikipedia:Reference desk/Mathematics#Penrose tiles puzzle pieces. Best. -- Toshio Yamaguchi 13:00, 7 March 2013 (UTC)

Hello. Why article Sergey Zonenko seen at "being considered for deletion"? Whay we can fix that article was not removed? — Preceding unsigned comment added by Ogeldke (talkcontribs) 11:42, 3 February 2015 (UTC)

## Examples of convolution

I saw the wiki page, but I couldn't find any examples using actual numbers evaluating the formula. Could you give some examples of convolution, please? Mathijs Krijzer (talk) 22:14, 9 March 2013 (UTC)

#### Definition

The convolution of f and g is written fg, using an asterisk or star. It is defined as the integral of the product of the two functions after one is reversed and shifted. As such, it is a particular kind of integral transform:

 ${\displaystyle (f*g)(t)\ \ \,}$ ${\displaystyle {\stackrel {\mathrm {def} }{=}}\ \int _{-\infty }^{\infty }f(\tau )\,g(t-\tau )\,d\tau }$ ${\displaystyle =\int _{-\infty }^{\infty }f(t-\tau )\,g(\tau )\,d\tau .}$       (commutativity)

#### Domain of definition

The convolution of two complex-valued functions on Rd

${\displaystyle (f*g)(x)=\int _{\mathbf {R} ^{d}}f(y)g(x-y)\,dy}$

is well-defined only if f and g decay sufficiently rapidly at infinity in order for the integral to exist. Conditions for the existence of the convolution may be tricky, since a blow-up in g at infinity can be easily offset by sufficiently rapid decay in f. The question of existence thus may involve different conditions on f and g.

#### Circular discrete convolution

When a function gN is periodic, with period N, then for functions, f, such that fgN exists, the convolution is also periodic and identical to:

${\displaystyle (f*g_{N})[n]\equiv \sum _{m=0}^{N-1}\left(\sum _{k=-\infty }^{\infty }{f}[m+kN]\right)g_{N}[n-m].\,}$

#### Circular convolution

Main article: Circular convolution

When a function gT is periodic, with period T, then for functions, f, such that fgT exists, the convolution is also periodic and identical to:

${\displaystyle (f*g_{T})(t)\equiv \int _{t_{0}}^{t_{0}+T}\left[\sum _{k=-\infty }^{\infty }f(\tau +kT)\right]g_{T}(t-\tau )\,d\tau ,}$

where to is an arbitrary choice. The summation is called a periodic summation of the function f.

#### Discrete convolution

For complex-valued functions f, g defined on the set Z of integers, the discrete convolution of f and g is given by:

${\displaystyle (f*g)[n]\ {\stackrel {\mathrm {def} }{=}}\ \sum _{m=-\infty }^{\infty }f[m]\,g[n-m]}$
${\displaystyle =\sum _{m=-\infty }^{\infty }f[n-m]\,g[m].}$       (commutativity)

When multiplying two polynomials, the coefficients of the product are given by the convolution of the original coefficient sequences, extended with zeros where necessary to avoid undefined terms; this is known as the Cauchy product of the coefficients of the two polynomials.

## How to request IP block exemption

I saw your post at WP:VPT. It appears that WP:UTRS is currently down due to toolserver problems. Your best bet is to try Wikipedia:Sockpuppet investigations#Quick CheckUser requests. Thanks, EdJohnston (talk) 04:13, 13 April 2013 (UTC)

Thanks. I didn't know about this. Wikipedia has obviously become too large and complex for me to handle :-) Sławomir Biały (talk) 19:58, 13 April 2013 (UTC)

## About axiom of global choice

Hello, Sławomir, I replied to you last comment here: http://en.wikipedia.org/wiki/Wikipedia_talk:Articles_for_deletion/Axiom_of_global_choice Eozhik (talk) 06:07, 22 April 2013 (UTC)

## Talk: Manifold

[1] No. You apparently do not understand the difference between the ring Z of integer numbers, which is a specific ring, and the ring of integers OK of a number field K, not a specific ring but a functor from fields(?) to commutative rings. Of course, the ring of integers of p-adic numbers contains some extra elements which Z does not have. Incnis Mrsi (talk) 06:18, 22 April 2013 (UTC)

Oh, indeed! You presume quite a lot about what others do not understand, while in the same breath betraying your own ignorance of the very subject that you would presume to "correct" me on. Thanks, but I'll pass. Sławomir Biały (talk) 13:49, 22 April 2013 (UTC)

## Another wiki

Being "semi-retired" here, you could be welcome there. Boris Tsirelson (talk) 07:23, 22 April 2013 (UTC)

## Transpose: best abstract definition?

If you feel that way inclined, I'd appreciate a quick "yes" or "no" at Talk:Transpose#Transpose_of_linear_maps: why defined in terms of a bilinear form?. — Quondum 14:17, 1 June 2013 (UTC)

Thank you very much for your answers to my question. I've learned many from you. Could you please make some comments on my newly posted words about the angle in Wikipedia:Reference desk/Mathematics? Thanks. Armeria wiki (talk) 03:38, 13 June 2013 (UTC)

## Banach space article

Dear Sławomir, Thanks for your comments and your interest for the Banach space article. I certainly agree with your comments, and I reply here because what I want to say is a bit personal. Actually, I would like some help of yours on the following points:

I don't feel like rewriting a lead in English. I can manage talking to mathematicians, but not to "a general audience".
I started writing a primitive sketch for an Introduction, but was blocked by the same language barrier. It was something like:
Introduction
Functional analysis aims to find functions that are solutions of various equations, several arising from physics. Abstract solutions, namely, functions that cannot be expressed by an explicit formula, are often obtained as limits in a well chosen vector space of functions X of a sequence of approximate solutions. Completeness of X is needed in order to make sure that the limit exists in X. Many examples of such spaces X, but not all, are Banach spaces.
Various type of compact sets in function spaces (norm compact, weak compact) are also used to prove the existence of abstract solutions, for example to optimization problems. In this respect, it is important to characterize compact subsets of function spaces.
I would like to have a section on differential equations in "Banach space", but I am not expert about this.

With best wishes, Bdmy (talk) 12:59, 17 June 2013 (UTC)

Hi Bdmy, I didn't mean to lay the task of improving the article entirely at your feet, just to suggest directions in which I think the article needs to be expanded. These are tasks that I wish I myself had time to undertake. Your mathematical edits to that article are most appreciated. There is now a solid foundation on which to build. Best, Sławomir Biały (talk) 17:45, 17 June 2013 (UTC)

## Apparent censorship of talk page

Sorry didn't mean it like that. I just thought that whole conversation was rather long and nothing to do with the talk page and had many insults and ad hominem attacks plus defences against those attacks - and thought it would be tedious reading for others. I hid lots of my own content as well with those tags. I have nothing to hide, just thought the whole conversation would be off topic for most readers.

But am probably not the best one to make a decision of what should be hidden if any :) Robert Walker (talk) 16:29, 11 July 2013 (UTC)

As someone who has in the past been the subject of invective from other editors, I sympathize. But I think it is a bad idea to hide comments directed against oneself (unless they are clearly trolling edits and there is likely to be a strong consensus to do so). Generally, it's usually best to let the comments stand. If there is a valid point, then it should be allowed to be seen; if it's just meaningless insults, these are typically easy to discern by other readers as well, most of whom do not take well to insults being hurled at other editors regardless of the circumstances. But hiding the comments of some editors in an apparent attempt to avoid engaging is clearly wrong, especially if you were the one who initially canvassed multiple projects. Some of this is officially recommended in the WP:NPA policy, but this is my personal take on the matter.
To the larger issue: I think a more productive course of action, and one that would be much more likely to bring in informed input than your current strategy, would be to start a formal request for comment. It is very important in such matters to be succinct, and I think you sometimes have difficulty with that. But I would fully support such an RfC if you're willing to go down that route. I can help you to set this up if you want me to, but maybe you should contact a more sympathetic party first (e.g., User:Wavelength, who is a very experienced Wikipedian as well). Sławomir Biały (talk) 17:03, 11 July 2013 (UTC)
Thanks, yes that's okay. I understand now.
BTW, I know two wrongs don't make a right but BI and WP frequently hide my conversations on talk pages, or archive discussions while still open. I suppose I got the idea about cot and cob tags being okay because it has happened so much in those conversations it came to seem normal. I know it isn't now. Robert Walker (talk) 23:17, 11 July 2013 (UTC)
I tried a RfC in the past, for a related topic, but it didn't work well at all, and it's put me off trying it here. Battery Included insults me and pays no attention to the reasons I give, and the whole thing puts off anyone else who wants to comment on it. [[2]]
Warren Pratts behaves almost identically to Battery Included, to the extent that I suspect them of being meat or sock puppets (due not just to the way they act, but many other strange coincidences). Whether they are or not, I think that RfC gives a pretty good idea of how it would go.
Any other thoughts do say, and thanks for the offer. I expect WP will find this conversation soon and start insulting me here, so probably will have to give up this discussion soon. Wavelength suggested trying again a year or so from now, meanwhile would continue editing wikipedia of course but just keep away from any topics to do with contamination issues. Difficult to do though when I'm on wikipedia every day and can see what is happening to a topic I care about. Robert Walker (talk) 17:32, 11 July 2013 (UTC)

## ArbCom

Hi. Just letting you know I've quoted a diff of yours at ArbCom in the Mars case. Someone not using his real name (talk) 17:39, 15 July 2013 (UTC)

## Any Thoughts ?

Wikipedia:Reference desk/Archives/Mathematics/2013 July 6#Convergence and Closed Form Expression. — 79.113.213.214 (talk) 00:10, 17 July 2013 (UTC)

## Reverted edition of dot product

Hi,

I am writing in response to your reversal regarding the dot product notation in Hilbert space:

The inputs of the dot product are vectors of the same type. Undid revision 565343587 by Elferdo

I understand your point, and don't object to the reversal. Maybe I should have discussed the notation before editing, I apologize.

However, I feel that your argument comes more from a programming notion of vectors than from a mathematical point of view. In fact, to me vectors (of the same vector space) in the mathematical sense don't have types, so the fact that a vector is represented with a column syntax or a row syntax does not change the vector to which that syntax refers.

This said, it is true that row or column syntax of vectors does affect the kind and the order of the operations that may be performed on them. But this is only a matter of representation, not of "vector type". To me, writing the dot product in euclidean spaces as a product of matrices feels more natural, because it follows the laws of matrix multiplication. For other definitions of the dot product usually the angle bracket notation <·, ·> is preferred.

So, to conclude, I would like to ask if the current notation is a standard, or if there are any reasons to prefer it over matrix multiplication notation. If so, could you please provide any references?

Thank you very much, Elferdo (talk) 13:49, 23 July 2013 (UTC)

A row vector and a column vector lie in different vector spaces. The dot product accepts vectors in the same vector space. It's not the same thing as the matrix product of row and column vectors. Sławomir Biały (talk) 14:53, 23 July 2013 (UTC)
Well, I will accept that row and column vectors lie in different vector spaces, but they happen to be dual and isomorphic. I suggest you take a look at this other wikipedia page: https://en.wikipedia.org/wiki/Row_vector#Operations. Since those two different vector spaces that you mention are isomorphic, we could think of them as being actually only two different representations of the same vector space. Then, in fact, scalar product in euclidean spaces, which was the original context of my argument, can be written as the matrix product of the row representation of the first vector and the column representation of the second vector.
If you can prove me wrong, then I would suggest that both pages of Row vector and Column vector be modified accordingly. Elferdo (talk) 17:39, 23 July 2013 (UTC)
The two spaces are naturally dual to one another, but this has nothing to do with the dot product. They are also not representations of the same vector space. They are nonisomorphic representations of GL(n). Sławomir Biały (talk) 00:46, 24 July 2013 (UTC)

## Proposed deletion of Functional notation

The article Functional notation has been proposed for deletion because of the following concern:

Possible copyright violation. This is just cut-and-pasted from the reference.

While all constructive contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the article to address the issues raised. Removing {{proposed deletion/dated}} will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Bill Cherowitzo (talk) 22:22, 30 August 2013 (UTC)

Thank you for the notification. I was not the original editor who added this to the project: I only moved it from functional (mathematics), where it obviously did not belong. It is most worrying that this was copied word-for-word from the source. Since forking out that content, I have noticed a number of alarming issues with the edits of the user in question. I have notified WT:WPM of these issues, although I suspect that an escalation to WP:AN is likely to be warranted in the near future. Thanks again for your vigilance, Sławomir Biały (talk) 22:49, 30 August 2013 (UTC)

## Functional notation

Hello, Sławomir Biały. You have new messages at Wcherowi's talk page.
Message added 22:57, 30 August 2013 (UTC). You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

## It makes no sense to define a Taylor series of a function on an arbitrary field.

Generalizing is usually good in mathematics. Talking about real or complex only numbers looks awkward, specially when this holds also for function over finite fields. AgadaUrbanit (talk) 23:51, 4 September 2013 (UTC)

No, it most definitely does not make sense over finite fields! Sławomir Biały (talk) 23:53, 4 September 2013 (UTC)
I'm not an expert, but here is the source @ 44m25s updated with more exact link. AgadaUrbanit (talk) 00:15, 5 September 2013 (UTC)
I may have missed something, but he only seems to discuss polynomials. Moreover, even for polynomial functions what he says is false over finite fields, despite his off the cuff claim at 44m25s. The derivative of a function on a field with p elements is not well-defined, all "derivatives" (in his sense) of the polynomial xp vanish identically, but the derivatives of the polynomial x are not all zero. However, as functions xp = x. Let's just stick to what standard, reliable sources, have to say on the matter. YouTube videos are not acceptable. There are thousands of textbooks written by authorities in the subject that define the Taylor series. Almost all of these define it over the real or complex field, so this is the case that deserves the WP:WEIGHT.
Incidentally, even in complete fields (over non-Archimedean places), usually one does not talk about differentiability at all, although it certainly makes sense to, since the derivative is an essentially useless concept there, to say nothing of the Taylor series. (In fact, a function can be given as a convergent power series, but not equal to its "Taylor series" at any point!) Sławomir Biały (talk) 00:53, 5 September 2013 (UTC)
Yup, you're right he talks about polynomials only, so I agree the claim does not hold for arbitrary function Taylor series discussion. Though not sure about your "The derivative of a function on a field with p elements is not well-defined," So yes, in your example, f(x) = xp = x, i.e. f(x) is the identity function. A derivative of the identity function is a constant function with value '1', as expected. What's not well defined in that? AgadaUrbanit (talk) 01:49, 5 September 2013 (UTC)
The derivative of the polynomial ${\displaystyle x^{p}}$ is ${\displaystyle px^{p-1}}$. This is identically zero for the field of p elements. But as a function ${\displaystyle x^{p}=x}$ and the derivative of the polynomial x is just 1. So it's meaningless to talk about the derivative of a function on a finite field. Sławomir Biały (talk) 12:16, 5 September 2013 (UTC)
You are correct here, the first derivative is zero. Wildberger reviews ${\displaystyle x^{p}}$ case. He defines the k-th sub-derivative as the k-th coefficient in Taylor series. According to him, all sub-derivatives from the first till the p-1 are indeed zero, but the p-th sub-derivative is actually 1. We have to be prepared to think a little bit differently he says. AgadaUrbanit (talk) 21:34, 6 September 2013 (UTC)
The first derivative of the function ${\displaystyle f(x)=x^{p}=x}$, if it is well defined, is either zero or not zero. Which is it, then? Sławomir Biały (talk) 22:59, 6 September 2013 (UTC)
There is a bit of contradiction here, but we have to consider bigger fields. Polynomials are not entirely functions in this sense. Calculus gives different derivatives, since those polynomials are different over power of ${\displaystyle p}$ field ${\displaystyle p^{n}}$. So derivatives of polynomials ${\displaystyle x^{p}}$ and ${\displaystyle x}$ just don't have any choice but to be different, despite the annoying fact that as functions ${\displaystyle x^{p}}$ and ${\displaystyle x}$ are indistinguishable over field ${\displaystyle p}$ AgadaUrbanit (talk) 23:59, 6 September 2013 (UTC)
The problem lies not in the field, but in the idea of thinking of polynomials as functions. Polynomials over general fields should not be thought of as functions to begin with. Then the polynomials ${\displaystyle x}$ and ${\displaystyle x^{p}}$ are distinct, and their formal derivative makes sense. The error lies in assuming that this has anything to do with the conventional differential calculus, despite what Wildberger would like you to believe. Sławomir Biały (talk) 12:08, 7 September 2013 (UTC)
I have been following this discussion with interest. There is another approach to resolving the apparent contradiction that can be defined on functions, applicable to a discrete domain. Wildberger is attempting to define the derivative in terms of the coefficients of the Taylor expansion of a function. It is natural to restrict this expansion to a basis (say) {bk: bk = (xa)k},aliasing occurs if not a basis. The crucial restriction on k is not unique, we could choose any basis (not only polynomials), and the definition of the "derivative" may vary depend upon the choice. Requiring further properties (e.g. the product rule) might severely limit this restriction, but assuming a basis as given with k∈{0,...,n−1}, we get a definition presumably valid for all/many commutative rings on functions (as opposed to on abstract polynomials). — Quondum 16:53, 7 September 2013 (UTC)
Ok. See "DiffGeom7: Differential geometry with finite fields". Talking about derivative of a polynomial function over a finite field makes sense according to to a source, despite your personal opinion that it is a nonsense. Your understanding of WP:RS is really lacking. You are wrong about YouTube videos are not acceptable. Youtube is only an archive and not a source, see Wikipedia:Video links. The source in this particular case is N J Wildberger He holds Yale University PhD from 1984. and taught at Stanford University (1984-1986) and the University of Toronto (1986-1989) before coming to UNSW (University of New South Wales), So the source looks good to me. AgadaUrbanit (talk) 01:48, 6 September 2013 (UTC)
You are absolutely wrong that the derivative of a function over a finite field makes sense. I have already given excellent factual reasons why this is true, but then you dismiss them as "personal opinion" (an obvious ad hominem). In that next video that you sent me, he seems to be talking about polynomials, not polynomial functions. As I've already indicated, these are not the same thing: ${\displaystyle x}$ and ${\displaystyle x^{p}}$ are different polynomials, but the same function. Wildberger seems to gloss over this distinction. Perhaps he is unaware of it, as expressions like ${\displaystyle D^{k}f/k!}$ that he loves to write obviously make no sense as written if k ≥ p (with a little work one can make sense of these, but he doesn't appear to try). It's more likely that he can't be bothered to mention any mathematical details that inconveniently don't fit his preconstructed narrative.
But anyway, what he calls differential geometry is not what almost anyone else would call that. They would call it algebraic geometry. One of the telltale features is that all "functions" are actually polynomials. But again to do algebraic geometry properly, one needs to introduce a whole lot of commutative algebra, something which obviously doesn't fit his narrative.
Finally, while there is certainly no bright line rule about using self-published sources like YouTube videos, these are usually not considered to be reliable sources absent contravening reasons. In this case, the views that you are using the video to support are sufficiently outside the mainstream that they do raise a WP:REDFLAG (which is policy). I certainly see no reason that these views deserve to be given more weight in an encyclopedia article than the thousands of published peer-reviewed sources that exist on the Taylor series: that obviously requires significant sources per WP:WEIGHT (which is also policy). Sławomir Biały (talk) 11:42, 6 September 2013 (UTC)
Sławomir, live long and prosper ;) I probably was not clear, apologies. I hoped you'd be amused by applying Calculus to finite fields, I certainly was. Wildberger does mention the issue with ${\displaystyle D^{k}f/k!}$, where k ≥ p. Nobody wants to divide by zero. My point is I'm just requesting you not to remove N J Wildberger references, as you did here, just because it is a Youtube link. Hope you see my point. Again, May the Force be with you. AgadaUrbanit (talk) 13:21, 6 September 2013 (UTC)
Ok, sorry. That source can probably stay, but I'd much prefer it to be replaced by a more conventional source. You can add it back if you want. Sławomir Biały (talk) 13:53, 6 September 2013 (UTC)

Thanks for commenting on the AdS/CFT article. I just wanted to let you know that I've made some changes in response to your comments. Let me know if it's what you wanted. Thanks again. Polytope24 (talk) 01:16, 27 October 2013 (UTC)

## tensor product

Hi,

I notice that ypou just reverted a fix I attempted on tensor product of Hilbert spaces. I made the fix mostly because I could not parse the formula there as written, and tried to replace it with something close to the original intent. FWIW, I made exactly the same change to tensor product. Basiclly, the issue is that the arrow w.r.t. the element of symbol: if x^* is an element of H^* then what the heck does x^* \to x^*(x_1)x_2 mean? The intent seemed to be to use a mapto not a \to. Or perhaps the orig author meant H_1^* \to x^*(x_1)x_2 but this doesn't make much sense either. I'm going to copy this over to the talk page there. Thanks. User:Linas (talk) 14:06, 23 November 2013 (UTC)

Yes a mapto is what was intended there. The morphisms associates to an element x^* of the dual of H_1 an element x^*(x_1)x_2 of H_2. Sławomir Biały (talk) 14:12, 23 November 2013 (UTC)
Czesc, yes, I understand the intent of what is happening there. The problem is that the notation is weird/wrong; its just not written correcty. See talk page there, please. User:Linas (talk) 14:27, 23 November 2013 (UTC)

## Am I doing this right?

This seems to jump the shark a bit, even though it ultimately produces the correct result. It would be nice if my method could be justified by complex analysis.--Jasper Deng (talk) 20:31, 20 December 2013 (UTC)

I don't really follow your way of eliminating the error term. But your original approach to the problem is a very natural one, and it strongly suggests first multiplying by a Gaussian ${\displaystyle e^{-(x^{2}+y^{2})\epsilon }}$ and then letting ${\displaystyle \epsilon \to 0}$. The integral
${\displaystyle \int _{I}e^{-\epsilon (x^{2}+y^{2})}\cos(x^{2}+y^{2})\,dx\,dy}$
can be easily computed in polar coordinates. Since the integrand now decays exponentially, the improper integral is no longer a problem. (Likewise with the sine integral.) On the right hand side of the two equations, the integrals of the form ${\displaystyle \int _{0}^{\infty }e^{-\epsilon x^{2}}\cos(x^{2})\,dx}$ (likewise with sine) converge to the appropriate Fresnel integrals (in this case ${\displaystyle \int _{0}^{\infty }\cos(x^{2})\,dx}$) as ${\displaystyle \epsilon \to 0}$. There is a slight trick to proving this last statement. Sławomir Biały (talk) 14:58, 21 December 2013 (UTC)
The error term elimination I was trying was relying on the notion that ${\displaystyle \lim _{x\to \infty }\cos(x)=\lim _{x\to \infty }\cos(x+\pi )}$. But the first notion is probably incorrect, even though both are taking the limit as the argument of cosine goes to infinity.--Jasper Deng (talk) 20:15, 22 December 2013 (UTC)

## Dot product and inner product

I do not understand your revert of my edit in dot product. I understand that you consider that "dot product" has to be used for coordinate vectors, and "inner product" refers to Euclidean vector spaces. This is not the convention used presently in this article. More specifically, the sections "Geometric definition", and "Scalar projection and the equivalence of the definitions" are about inner product (called here "dot product") of Euclidean vector spaces. Before my edit and after your revert, the section "Scalar projection and the equivalence of the definitions" passes suddenly from Euclidean vectors to the standard basis of Rn without saying that this can not be done without choosing an orthogonal basis of the Euclidean vector space. This is not only confusing (see the recent good faith edits by an IP user and my comment on his talk page), but mathematically incorrect. My edit was intended to restore mathematical correctness. I agree that the article needs further edits for clarifying the terminology, splitting the section "Scalar projection and the equivalence of the definitions" into "Scalar projection", "Properties" (bilinearity) and "Equivalence", etc. But, in any case, mathematical correctness comes before accurate terminology. Therefore, I'll revert your revert, hoping that you or someone else will clarify the terminology, and adapt accordingly the articles dot product and inner product space. I cannot do it myself, because, for me, "dot product", "scalar product" and "inner product" are synonyms (by the way, the term "dot product" does not exist in French, and "produit intérieur", the equivalent of "inner product", is rarely used; this is not a problem). D.Lazard (talk) 15:19, 8 January 2014 (UTC)

The "dot product" is specifically defined in Rn. It is the sum of the products of the components of an n-tuple. This is how the term is used in English, and the usage in the article is in agreement with the vast majority of quality sources (including those aimed at a wide variety of mathematical levels). Sławomir Biały (talk) 15:29, 8 January 2014 (UTC)
It is also remarkable that most math editors, even those proficient in “real/Euclidean space”, “dot/inner product”, “affine/linear function/polynomial”, and similar pettifogging, usually ignore existence of the real coordinate space article. Incnis Mrsi (talk) 15:32, 8 January 2014 (UTC)
I agree that "dot product" is specifically defined in Rn. But, this article does not apply this convention. Applying this convention would imply to move the sections "Geometric definition" ,"Scalar projection and the equivalence of the definitions", "Application to the cosine law" and "Physics" to Inner product, and replaced by a section "Relation with inner product". The redirect scalar product should also be edited. D.Lazard (talk) 15:57, 8 January 2014 (UTC)
I disagree with this proposal. The standard treatment of the dot product is to include both an algebraic definition (via coordinate vectors in Rn) and a geometric definition. Many reliable sources define it each way, and derive the other. See Talk:Dot product for a list of sources by such mathematical luminaries as Josiah Willard Gibbs, Paul Halmos, Richard Courant, Peter Lax, and Tom Apostol. Also, many such sources include a discussion of the cosine law. Not to include this basic information would be a serious omission. Sławomir Biały (talk) 16:28, 8 January 2014 (UTC)

## Taylors Theorem Revert

For readabiliy it is a good idea to separate out the history section. Also you reverted the fix for the "passive voice" weird grammar used.

"Taylor's theorem is named after the mathematician Brook Taylor, who stated a version of it in 1712. Yet, an explicit expression of the error was provided much later on by Joseph-Louis Lagrange. An earlier version of the result is already mentioned in 1671 by James Gregory.[1]"

There is an implicit statement here that Brook Taylors version did not have an error term. Implicit statements are not very readable because they create doubt in the readers mind. In my mind the above writing would be unacceptable for a primary school student. It is affected and pretentious. You could have corrected what you saw as wrong, but you chose just to roll it back. I will not play revert wars with you. Do as you will. Large numbers of mathematics articles are burdened with affected and pretentious language, which makes them inaccessible for the average reader. The wiki is not just for experts. It is a general encyclopedia. Of course expertise will always be valued, but effective communication is just as important.

Thepigdog (talk) 04:16, 10 February 2014 (UTC)

Ok, but as far as I can tell you didn't copy edit the content to remove this perceived ambiguity. (In fact, you didn't seem to copy edit the material at all. Nor did you even include an informative edit summary.) I have no problem if you want to write a separate "History" section. I can recommend some sources that should get you started on that project, if you're interested. But namesakes for eponymous discoveries generally belong in the lead of the article. Sławomir Biały (talk) 12:55, 10 February 2014 (UTC)
Hello, Sławomir Biały. You have new messages at Dolphin51's talk page.
You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.
This is not the right page for me to make any changes to.
Respectful regards Thepigdog (talk) 06:09, 12 February 2014 (UTC)

## Wikipedia:Reference_desk/Mathematics#Jacobians_and_vector_field_differentials

I was thinking you could help answer this question that I asked in lieu of a proper tensor calculus/algebra or differential geometry textbook.--Jasper Deng (talk) 04:57, 16 March 2014 (UTC)

## Holomorphic functions: context goes first

Hey. Thanks for correcting any mistakes that I did there. Just want to know how do you decided that 'are the central object in complex analysis ' goes first than the actual meaning of the term?

I accept i missed correcting grammar there, but i think 'In mathematics' is good enough context for a topic like holomorphic functions.

Mittgaurav (talk) 04:30, 21 March 2014 (UTC)

Usually, we would want to include somewhere in a neighborhood of the first sentence that holomorphic functions are part of complex analysis, indicating not just that mathematics are involved but the area of mathematics that the topic is relevant to. This is essentially the way all of our mathematics articles are patterned. Not every reader may know anything about the topic at all, nor even whether they have arrived at the right page. For instance, someone might be looking for an article on homomorphisms, which are a part of algebra rather than analysis, and accidentally hit the page holomorphic function. Sławomir Biały (talk) 12:19, 21 March 2014 (UTC)

cool. makes sense. thanks! Mittgaurav (talk) 16:54, 21 March 2014 (UTC)

## Wikipedia talk:Manual of Style/Lead section#WP:BOLDTITLE and election articles

I have started a discussion that may interest you at Wikipedia talk:Manual of Style/Lead section#WP:BOLDTITLE and election articles. Anomalocaris (talk) 08:09, 3 April 2014 (UTC)

## Formal mediation has been requested

 The Mediation Committee has received a request for formal mediation of the dispute relating to "Tensor". As an editor concerned in this dispute, you are invited to participate in the mediation. Mediation is a voluntary process which resolves a dispute over article content by facilitation, consensus-building, and compromise among the involved editors. After reviewing the request page, the formal mediation policy, and the guide to formal mediation, please indicate in the "party agreement" section whether you agree to participate. Because requests must be responded to by the Mediation Committee within seven days, please respond to the request by 14 April 2014. Discussion relating to the mediation request is welcome at the case talk page. Thank you. Message delivered by MediationBot (talk) on behalf of the Mediation Committee. 15:36, 7 April 2014 (UTC)

## Rational Pricing Discussion

Dear Slawomir,

I started a discussion thereabout on Rational Pricing because you reverted my edit.

Duxwing (talk) 13:34, 11 April 2014 (UTC)

## Request for mediation rejected

 The request for formal mediation concerning Tensor, to which you were listed as a party, has been declined. To read an explanation by the Mediation Committee for the rejection of this request, see the mediation request page, which will be deleted by an administrator after a reasonable time. Please direct questions relating to this request to the Chairman of the Committee, or to the mailing list. For more information on forms of dispute resolution, other than formal mediation, that are available, see Wikipedia:Dispute resolution. For the Mediation Committee, Sunray (talk) 05:47, 12 April 2014 (UTC) (Delivered by MediationBot, on behalf of the Mediation Committee.)

## A quickie

Hi Sławomir!

Could you confirm or refute the correctness of the following?

If a representation Π of a Lie group G is not faithful, then N = ker Π is a nontrivial normal subgroup. There are three relevant cases cases:
1. N is non-discrete and abelian.
2. N is non-discrete and non-abelian.
3. N is discrete. In this case NZ, where Z is the center of G.
In the case of SO(3, 1)+, the first case is excluded since SO(3, 1)+ is semi-simple. The second (and first) case is excluded because SO(3, 1)+ is simple. The connected component of the Lorentz group is isomorphic to the quotient SL(2, C)/{I, −I}. But {I, −I} is the center of SL(2, C). It follows that the center of SO(3, 1)+ is trivial. This excludes the third case. The conclusion is that every representation Π:SO(3, 1)+ → GL(V) and every projective representation Π:SO(3, 1)+ → PGL(W) with V, W finite-dimensional vector spaces are faithful. YohanN7 (talk) 16:33, 21 April 2014 (UTC)

I think I have references to back it up, except for the conclusion (reps are faithful), but these references are 500 km away at the moment. The Wikipedia articles don't suffice. I'd appreciate your help. YohanN7 (talk) 16:33, 21 April 2014 (UTC)

Yes, that seems correct. Sławomir Biały (talk) 10:07, 22 April 2014 (UTC)
Thanks! YohanN7 (talk) 02:45, 23 April 2014 (UTC)

## Notice of RfC 2 and request for participation

There is an RfC on the Gun politics in the U.S. talk page which may be of interest to editors who participated in "RfC: Remove Nazi gun control argument?" on the Gun control talk page.

Thank you. --Lightbreather (talk) 15:29, 26 April 2014 (UTC)

## Limit

What does this mean? Why should the arrow be pointing downwards?

${\displaystyle \lim _{\varepsilon \downarrow 0}\int _{-\varepsilon }^{\infty }}$

SmiddleTC@ 10:11, 5 May 2014 (UTC)

It's a common notation for a one-sided limit. Sławomir Biały (talk) 11:35, 5 May 2014 (UTC)

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## Response: Beal's Conjecture

Hi, I am sorry not to give reasons for my edit of Beal's Conjecture's known cases, but the room allowed there did not make a response possible. I am fairly new to Wikipedia, and am not sure if this is the appropriate place to give the reason, but I will. The paper cited does claim a proof of the (n,n,3) case, but does not make it explicit because it is so immediately apparent from how it is stated there. In fact, for this reason, it is not likely that a published paper will make this explicit. If n>2, then k divides n, where k is prime or 4. If A and B are part of a counterexample with exponents (n,n,3), then they can be raised to the power of n divided by k and therefore pertain to a counterexample of the form (k,k,3), contradicting the results as explicitly stated in the cited paper. By the same reasoning, in the (n,n,2) case for n not a 2 power or 3, n is divisible by 6, 9, or some prime greater than 3, and this factor can be taken as k in an argument like the one above. This is not a new result, just a less than clearly result already attained as stated in the paper already cited. However, I assume the author expected serious researchers in the area of the conjecture (the intended audience of the paper), would immediately see these claims as included therein. — Preceding unsigned comment added by Kyle1009 (talkcontribs) 18:33, 19 June 2014 (UTC)

I see, yes. As the old joke goes, "Ah... It's trivial".  :-) Sławomir Biały (talk) 19:30, 19 June 2014 (UTC)

## Remember BLP applies to all content including essays

Dzień dobry!

As a friendly recommendation, can you please try not to mention specific real-world (i.e. off-wiki) individuals by name in essays, when they or their families are being spoken about in a broadly negative fashion. I think this also applies to linking specific news stories. However, to get around this, I think you can provide sufficient contextual details that anyone with half a brain and access to Google can work out what you're talking about. This is because as I'm sure you understand WP:BLP applies to all pages, not only to articles.

Thanks, Barney the barney barney (talk) 09:25, 3 July 2014 (UTC)

Good point. My intention wasn't to write an essay, but rather to post something over at WT:RS once the whole AfD has blown over. I'm hoping it is still ok to comment on these sources, without implicating any living person, at least on the talk page. Sławomir Biały (talk) 11:02, 3 July 2014 (UTC)

Hi Sławomir, Thanks so much for your welcome message to me. The links you gave me are really helpful. Best wishes Fatootsed (talk) 21:03, 3 July 2014 (UTC)

## Tensor density

I have to say this.

The comment "Fine. If three PhDs agree that a "mass density" or "charge density" is not a density at all, clearly they must be right." you made to our crank over at the talk page wasn't very nice considering he seems to be a harmless crank with bad self-esteem. Now not only he, but also his professors are declared idiots in his mind now. I'm sure he's walking around talking about this. I actually feel sorry for him.

Besides, you are wrong, experienced professor or not, this time you are wrong. All densities are densities with the other convention as well, just stick to one convention per calculation and you'll be fine.

This is what I meant by a measure of religiosity on your part. No doubt JRSpriggs is even more religious. I'm actually very surprised. YohanN7 (talk) 05:14, 6 July 2014 (UTC)

Even this characterization seems overly harsh. Cranky, perhaps, but a crank, no. I can understand Sławomir's sarcasm in the circumstances, but I guess we should remember not to bite the newbies. —Quondum 06:11, 6 July 2014 (UTC)
Unthinking appeal to authority deserves to be called out, in my opinion. I see far too much of it, both on and off Wikipedia. If I'm cranky, that's why. Sławomir Biały (talk) 15:08, 6 July 2014 (UTC)
The guy came in with the firm unthinking belief that g had weight -2. He spent a month on a daily basis to change the article to that effect. When we finally got him to talk, it took a couple of days for him to realize (by himself actually) that there were two conventions. Then he got to hear that his and his professors convention was not only uncommon, but wrong. It is here that things went sour. Some effort has been made by SB and JR to argue that the alternative convention is wrong/unnatural, with or without quotation marks. These attempts have not been very successful. Whether you map the set of densities to numbers (so-called weights) with or without a minus-sign is pretty immaterial (or do you argue otherwise?). Yet, if you, like Weinberg, prefer the minus-sign, then you automatically agree that charge density isn't a density at all because such densities are "supposed to have weight 1", where that last clause appeals to your convention. Such reasoning isn't the very best if you want to keep the guy from "unthinking appeal to authority" because the alternative you offered there wasn't the most logically coherent.
I was convinced myself for a while that the alternative convention is flawed because of local authority (SB,JR). YohanN7 (talk) 16:21, 6 July 2014 (UTC)
If you want to adopted the convention that densities have weight -1, that's fine. But in mathematics there is a thing called the "bundle of densities", and this has a clear and unambiguous meaning that is not subject to any arbitrary choices. The weighted densities (for integer weights) are the tensor powers of this bundle. It is most natural to assign the weight as the number of tensor factors of this bundle. There appears to be no motivation at all for saying it should be minus that number of factors, and in fact such a convention leads to genuine confusion. It is in this sense that the convention of assigning densities a weight of -1 is "wrong". Sławomir Biały (talk) 17:56, 6 July 2014 (UTC)
No, I don't want to adopt the -1 convention. I wanted to make sure that we are talking about a valid convention and not something inconsistent that could be questioned on some mathematical/conceptual ground. It is still as far as I can see entirely equivalent to chose the negative of the number tensor factors of the bundle as a weight for those who want to do it (though I doubt that it is their primary motivation). I take your word for it that the other convention is impractical, perhaps even error prone. I just didn't want to leave with the false impression that the other convention has built in inconsistencies or is inadequate of handling all the things the +1 convention can handle. You can easily get this impression from the talk page
Thanks for explaining about the bundle. YohanN7 (talk) 19:04, 6 July 2014 (UTC)

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## Viewfinder (talk · contribs)'s behaviour

There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. Thank you.. Barney the barney barney (talk) 10:20, 7 August 2014 (UTC

## Jacob Barnett

You have reverted other editors at Jacob Barnett four times in the last 24 hours. Here are the diffs: [3] [4] [5] [6] Breach of the three revert rule. Viewfinder (talk) 22:59, 7 August 2014 (UTC)

It is not my intention to "edit war" with anyone, and I hope that my continued talk page participation has made this clear. I believe I have shown a willingness to explain my edits, and I am willing to work collaboratively with you, S. Marshall, Oleryhlolsson, Cunard, Agricola44, and anyone else. A number of these actions were not reverts, though. As you are no doubt aware, over the past two days I have edited the article extensively. This has not only included expanding the article by adding text, correcting references, and organizing content. The first two diffs that you listed was actually part of this series of edits, involving a significant expansion and restructuring of the content of the article. You can call this a "revert" if you wish, but even if you want to be so insistent at worst it is only a single revert, not two. In fact, at least some aspects of the structural changes that you initiated were incorporated into the final version. (A series of consecutive edits is not considered to be more than one revert.) Likewise, this edit part of this attempt to correct the misapprehension articulated in the previous edit summary that the statement was about Edwards, not Barnett. It also removed the claim that Edwards was an expert on child prodigies as unreferenced. That is a substantive change responding directly to the issues that were raised at the time, not a revert as I see it. The misunderstanding on the discussion page, as well as the fact that myself and the other editor involved got our replies mixed up, makes this clear enough, I should think. These are the kinds of things that happen when too many editors edit the same article at the same time: you yourself are guilty many times of deleting others' posts for, what I assume, is the same reason. The only edit that I unequivocally agree was a revert was this one. But even if you insist on counting all of these actions as reverts, it was precisely three. In any event, I think I have already demonstrated a willingness to work collaboratively, despite repeatedly having my motives vilified by certain persons. I actually do want the article to be as neutral a reflection on the subject as possible. Sławomir Biały (talk) 00:26, 8 August 2014 (UTC)
The first three diffs were all flagged up by my notifier as reverts. A revert does not cease to be a revert by being accompanied by other changes. As you are now fully engaging on the talk page I did not report the 3RR breach. I don't think blocking you would be helpful, even in the unlikely event that admin would do so. Viewfinder (talk) 15:08, 8 August 2014 (UTC)
Oh Viewfinder (talk · contribs) - aren't you so kind? Barney the barney barney (talk) 15:24, 8 August 2014 (UTC)
Viewfinder, as I said consecutive edits count as one revert, not two. So even on the most draconian reading of that policy, the sequence of edits you objected to is precisely three reverts. I suggest that you familiarize yourself with the policy before issuing such threats in the future. That is a good way to get yourself blocked for disruption. Sławomir Biały (talk) 15:58, 8 August 2014 (UTC)
Cut the sarcasm Barney. It's neither cool nor helpful. Viewfinder (talk) 18:01, 8 August 2014 (UTC)
Actually Viewfinder (talk · contribs) - what's not helpful is your patronising and threatening an experienced editor who has spent a great deal of patience and time trying (but failing) to explain (to you pretty basic and fundamental issues with Wikipedia policy and how basic science works. And you respond to this patience and understanding with a passive-aggressive note about edit warring. Barney the barney barney (talk) 19:43, 8 August 2014 (UTC)
There was a breach of 3RR which I felt that I was entitled to point out. Why don't you stop making personal attacks and revert to your recent helpful contribution to reaching consensus at Jacob Barnett? Viewfinder (talk) 19:52, 8 August 2014 (UTC)
Once again, I admonish you to stop accusing me of a 3RR violation; I implore you to read the guideline in question. In case you find the content in the obvious pink box there too nuanced to understand, there are a number of sentences that follow it in what appears to be plain English that even you should be able to comprehend. If this is not so, then I humbly submit that perhaps the task of writing an encyclopedia in the English language may not be your calling, and the turnip truck beckons. Sławomir Biały (talk)
There are three levels of response that you'll find you'll get Sławomir Biały (talk · contribs), let me take you through the next two to save you time:
1. You will be ignored and told you're wrong. Detailed arguments based on policy are wrong.
2. Viewfinder (talk · contribs) will WP:CHANGETHESUBJECT and accuse you of personal attacks, including perhaps raking up old complaints from other people whose incompetence you've had to previously suffer.
3. Viewfinder (talk · contribs) will delete any correspondence from you and pretend that you don't exist.
Barney the barney barney (talk) 21:10, 8 August 2014 (UTC)

## Response on compact space talk page.

Just so you are aware: I responded to your assertion on Talk:Compact space with a concrete example (i.e. the case of a non-Abelian distance metric, for which your interpretation would be false). — Preceding unsigned comment added by TricksterWolf (talkcontribs) 14:49, 12 August 2014 (UTC)

## Spinor

We seem to be in a minor edit war on the Spinor page. I have been editing the spinor on and off for years trying not too step on too many feet. I agree that there is still a lot of room for improvement. I have been trying not to step on too many feet for years, and that has certainly led to a suboptimal leader as the same material keeps being rehashed and brought back It is sort of refreshing that you tried to break through that, You were obviously not too thrilled when I reverted your labor of love that you have been obviously working on hard. I must admit though that I did not think your edits were overall positive. You put a lot of emphasis on the topological side of things, but I think your description of the class of the representation was confusing at best and mathematically gets the argument backwards at worst. You have a point that this is an important aspect so I have added that, but in a way that I think is more correct. I also think that the Clifford algebra point of view is important and not very well explained by what you wrote. Anyway i think there is now roughly the same material in as you put in there except, I believe, in more detail, more concise and more correct even though it is now slightly longer than what you wrote. SInce I had things written up while you reverted my revert I reverted yours once more if only not to get my changes lost. I am sure we can work out differences. We both seem to have a mathematical background, and I think we both try to give a description that is precise even though I think we also try to remain intelligible for physicists, so I think we should be able to work out the differences.

P.s. I also find the animated GIF of the belt trick rather distracting but this time I left it in so as not to fight over things that are easily done later. P.P.s. What I REALLY would like to get rid of in this article, or change completely, are the examples in dimension 2 and 3 and 4, showing how the different constructions mentioned work out there. P.P.P.s what I also think this article is really missing is a description of the invariant hermitian form and the Dirac invariants, which I guess is hidden in the Fierz identities but again is hardly obvious. RogierBrussee (talk) 21:41, 21 September 2014 (UTC)

There is discussion about the lead already taking place at Talk:Spinor, in a number of sections at the end. The last section concerns the most recent edits, and further discussion should take place there, not on my user talk page. Sławomir Biały (talk) 13:53, 22 September 2014 (UTC)

## Laplace Transform

Do you mind if we (or I) move your comment on my talk page to the talk section of Laplace Transform? It seems important, i.e. when an inverse LT is possible ... Thanks, DoctorTerrella (talk) 01:36, 23 September 2014 (UTC)

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## On the definition of e

Hi Sławomir,

you recently (essentially) reverted an (admittedly awkward) edit I made at E (mathematical constant) and I'd like you to reconsider it. My intention was to provide a clarification that I think is needed. Another editor had twice tried to change this definition and I thought that I understood why. The statement, as written, can be misinterpreted as saying that the exponential function is defined by the derivative condition at zero (and he pointed out that many functions have this property). What this editor was failing to see was that this condition singles out the exponential function from all the generalized exponential functions and thus defines "e". I thought to clarify this by explicitly talking about the generalized exponentials. The original phrasing (and the one you reverted to) gives the appearance of being circular, and you have to know the context in order to parse it correctly – not what you want in the lead of an elementary topic. If you agree, I wouldn't mind some help in doing a better job of getting this point across. Thanks. Bill Cherowitzo (talk) 18:12, 3 October 2014 (UTC)
Thanks. Bill Cherowitzo (talk) 20:54, 3 October 2014 (UTC)

Sławomir, your edits here are spot-on and achieved the desired result excellently, and I'm just adding this to show that this thread is clearly resolved. —Quondum 18:28, 11 December 2014 (UTC)

## Thanks for reminding on Riemann Curvature

Thanks for your reminding on the commuting assumption! --IkamusumeFan (talk) 17:03, 9 October 2014 (UTC)

## I'm sorry, but I vote only one time but you....

Dear Sławomir Biały,

I'm sorry, but I keep only one time but you.... Please see again: https://en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/Dao%27s_theorem. Thank to You very much.

*Keep I write this page as following form of Thébault's theorem based on some articles publish in some journal. I write this page with neutrality, no promotional Dao Thanh Oai(I can not write this page with another name because title of some articles at here is Dao's theorem.....) Please noting that Dao's theorem is theorem on Euclidean geometry, and these Journal is classical of Euclidean geometry. If these theorem is no notable theorem we should delete pages but Dao's theorem is nice and notable theorem(because it is generalization of some famous theorem), so I think we should keep and improvement of this pages.--Eightcirclestheorem (talk) 05:15, 5 October 2014 (UTC) User already voted. Sławomir Biały (talk) 12:20, 15 October 2014 (UTC)

Please see again, and please let me why you said that: I already voted?--Eightcirclestheorem (talk) 15:30, 15 October 2014 (UTC)

## A barnstar for you!

 The Random Acts of Kindness Barnstar Thanks for your contributions at the mathematics reference desk. They are much appreciated! Neuroxic (talk) 22:53, 18 October 2014 (UTC)

## edit warring

Please read the policy write one level down applied to clarifying articles, see my bold comments on the relevant talk page. Edits like this removing tags without addressing the underlying issue won't get the article posted to ITN. It can also constitute a violation of WP:3RR even if you have technically not reverted the article more than thre times.

You are formally warned of this, I won't post here any more, discussion should be kept on the article talk page. μηδείς (talk) 04:17, 16 November 2014 (UTC)

Your recent editing history shows that you are currently engaged in an edit war. To resolve the content dispute, please do not revert or change the edits of others when you get reverted. Instead of reverting, please use the article's talk page to work toward making a version that represents consensus among editors. The best practice at this stage is to discuss, not edit-war. See BRD for how this is done. If discussions reach an impasse, you can then post a request for help at a relevant noticeboard or seek dispute resolution. In some cases, you may wish to request temporary page protection.

Being involved in an edit war can result in your being blocked from editing—especially if you violate the three-revert rule, which states that an editor must not perform more than three reverts on a single page within a 24-hour period. Undoing another editor's work—whether in whole or in part, whether involving the same or different material each time—counts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit warring—even if you don't violate the three-revert rule—should your behavior indicate that you intend to continue reverting repeatedly. — Preceding unsigned comment added by Medeis (talkcontribs)

Frankly, this "warning" is totally out of line. I think you need to cool it, and also do some serious reflection on what the guidelines WP:JARGON and WP:MTAA actually say. Sławomir Biały (talk) 14:24, 16 November 2014 (UTC)

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## Unbalanced templates in your user page

Hi, I found you have a {{hab}} in the Articles to work on section with no corresponding {{hat}}. --CiaPan (talk) 15:29, 11 December 2014 (UTC)

Fixed [7] --CiaPan (talk) 10:21, 18 September 2015 (UTC)

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## Incivility and personal attacks

I do not understand why you always feel the need to respond to my contributions to Talk:Jacob_Barnett with personal insults. If my contributions are as incompetent as you claim, they will make no contribution to the article, so why don't you merely ignore them? Viewfinder (talk) 13:11, 22 December 2014 (UTC)

You have consistently demonstrated the same kind of incompetence in nearly every discussion that has taken place since the second AfD. Either you are a troll, incompetent at reading English (see earlier thread here), or you are pushing some agenda (and probably all three, based on my observations of months of continued interactions). If you don't want to get called out for this, probably you should stop editing the article. It's not as if I am stalking you. Sławomir Biały (talk) 15:04, 22 December 2014 (UTC)
Here you go again - this time accompanied with a threat. Viewfinder (talk) 16:47, 22 December 2014 (UTC)
I sense that there is a bridge somewhere that has been left unguarded. Better see to it... Sławomir Biały (talk) 16:58, 22 December 2014 (UTC)
What's that meant to mean? Viewfinder (talk) 17:01, 22 December 2014 (UTC)
I should have known. The lack of reading comprehension is strong with this one. Sławomir Biały (talk) 17:14, 22 December 2014 (UTC)
Some time ago I was well advised that "if they cannot make themselves clear, they should be ignored". Viewfinder (talk) 17:29, 22 December 2014 (UTC)
So you ignore everything you don't understand? That is most telling. Presumably, this explains why someone who is barely literate in the English language, incapable of processing even the most rudimentary metaphor, thinks that he or she should be editing an encyclopedia written in English. But competence is required to do that. So I suggest that you should leave the article alone, at least until you graduate from primary school. Sławomir Biały (talk) 17:40, 22 December 2014 (UTC)
If I don't understand, I ask for clarification. But all I got from you was yet another personal insult, the implication being that you are unable or unwilling to make yourself clear. That is why you should be ignored. Viewfinder (talk) 20:31, 22 December 2014 (UTC)
Ok, but you show every indication of understanding nothing. Every mundane point, obvious to everyone in the room but you, needs to get argued to death at Talk:Jacob Barnett, like what followed in your recent reversion of my edit. And yet, there when your obvious error was pointed out, you doubled down on the stupid. You persisted in arguing that there was something of encyclopedic value at the link in question. This is not an isolated incident either. (E.g., your denials of relativity theory, etc.) Viewfinder, WP:AGF is not a life sentence, and the truth is an absolute defense against WP:NPA. You are a net drain on this project, wasting the time of other productive editors. You are a useless troll whose incompetence we have all suffered quite enough of. The sooner you leave this place, the better. Sławomir Biały (talk) 21:27, 22 December 2014 (UTC)
You accuse me of denying relativity, and this is a public forum. Please withdraw or substantiate this claim. Viewfinder (talk) 21:34, 22 December 2014 (UTC)
It's not an accusation. It's a statement of fact. You repeatedly and vigorously defended the media sensationalism surrounding the story. The AfD and talk page are full of this kind of special pleading: "You seem to be suggesting that his mother may have been serially lying to reporters. They're surely not all that gullible and her claims are likely to be verifiable." "Surely if Mrs Barnett were as dishonest as some contributors (notably SB and DE) are implying, then that would have been exposed long ago and the media would have stopped publicizing her." You are challenging the reliability not just of the subject's mother, but of many internationally known publications, with plenty of fact checking resources. All of them are wrong and you are right? Strong stuff. "For the most part, I still maintain that he did think he had expanded relativity..." along with attestations that there was "some truth to" the media sensationalism. "Whether or not the material in question is fringe, it was written in publications that are certainly not fringe." This is classic POV-pushing denialism. Sławomir Biały (talk) 22:02, 22 December 2014 (UTC)
So if I am denying relativity, then so were the entire international broadsheet media. In the words of a contributor to the DRV, this is nonsense. Utter nonsense. Viewfinder (talk) 22:23, 22 December 2014 (UTC)
Wow, just wow. Yet another implicit defence of the "broadsheet" media sensationalism. Presumably, you were unable to read my post containing numerous examples of precisely this sort of thing in the media, helpfully organized because, as you said in that very discussion, you were unable to read the sources yourself and find these statements. If you have trouble reading the plain English words written that I wrote there, then I suggest that you pay someone to read them aloud to you, possibly after translating them into your native tongue. Sławomir Biały (talk) 22:46, 22 December 2014 (UTC)
Yes, I did defend the media and in particular the subject's mother against your ferocious comments, and that is why you think that I am too incompetent to be editing Wikipedia. Viewfinder (talk) 22:48, 22 December 2014 (UTC)
No. I think you're incompetent to be editing Wikipedia because you appear to be illiterate. Something is written down, and you deny it was written. A source says something, but you deny that it says it. When a comment you make is solidly and definitively rebutted, you continue to argue the same set of points, often doubling down on whatever your point happens to be. This penultimate post is just one example. But I think "variations on a theme" is something you are probably incapable of understanding. So let me make this very simple for you: You are too stupid to edit Wikipedia. Please go away. Sławomir Biały (talk) 23:10, 22 December 2014 (UTC)
Yes, of course. You are the truth, you are the whole truth, you are nothing but the truth, and everything else amounts to stupidity and/or malicious lies which should be banned. Incidentally my Mensa membership number is 61813. Viewfinder (talk) 10:10, 23 December 2014 (UTC)
Viewfiender, I could care less about whatever clubs you are a member of. It is a fact that you have systematically been unable to read content that conflicts with whatever inane babble you happen to spouting. This includes your utterly strange and vigorous assertions that the media never said that Barnett disproved and/or expanded Einstein, when even some of the headlines of references used in the article attested this. You have also shown every indication of being unable to read (or possibly remember) all of the many times the same things were explained to you by a number of different editors (Agricola, for one, who you seem to hold in high regard). This systematic pattern of your ignorance is there for everyone to see. It is not some post-modern abstraction, whereby I am entitled to some interpretation of the "truth" or whatever. Now a charitable, good-faith-based, interpretation is that you suffer from a severe intellectual handicap. You alluded to this handicap before, and it definitely shows in your contributions to the encyclopedia. But regardless of the reasons for your behavior, you are a net drain on productive editors' time, while yourself not contributing anything of value to the project. You should retire, for real. Your further input to Jacob Barnett is not useful. Sławomir Biały (talk) 13:46, 23 December 2014 (UTC)
Like Jacob Barnett, I am affected by Asperger's syndrome. If you think that that should disqualify me from contributing to his biography, then think again. And think again if you think I will be intimidated by your invective. Viewfinder (talk) 15:24, 23 December 2014 (UTC)
Fine. I take this as an admission that you are not editing in good faith, and that you will continue the disruption at the article in question, despite several warnings. Your future edits will be treated as such. Per your initial request not to be taken seriously, I will forgo any further interaction with you. My next stop will be ANI if your disruption continues, and I will argue very strongly for an indefinite block. Sławomir Biały (talk) 18:30, 23 December 2014 (UTC)
I have made no such admission, express or implicit. And arguing my case on an article talk page is not disruption. Stop the threats. Viewfinder (talk) 18:44, 23 December 2014 (UTC)
That is the only explanation left for your inability to read sources and posts, that you had the capacity to read them, but willfully chose not to. That is considered to be disruption. I can no longer assume that you are editing in good faith. Sławomir Biały (talk) 19:00, 23 December 2014 (UTC)

### redux

Moved here to usertalk from article-talk, per request.[8] 75.108.94.227 (talk) 22:26, 17 September 2015 (UTC)

Strike your accusations, Sławomir. If you need me to call them out, one by one, I'm happy to do so. You are free to be sick of the discussion; as already noted, you are the most prolific contributor to that talkpage, by far. You are not free to make insinuations. You've been on wikipedia long enough to know pillar four. Back in 2009, you used to think it was important. It still is important. 75.108.94.227 (talk) 22:26, 17 September 2015 (UTC)
I am likewise having difficulty in understanding the motivation of 75.108.94.227 RE Jacob Barnett because past discussions explored every nook and cranny and there are really no new substantive sources that say anything else. (I suspect JB's 15 minutes of fame have run their course, but that's a separate issue.) So far there has only been vague talk, but no actual proposals, thought I've started asking directly for same. Unless there's some forthcoming substance from 75.108.94.227, I think the discussion is about over. Agricola44 (talk) 15:16, 18 September 2015 (UTC).

## Two accounts?

Why the two accounts, User:Sławomir Biały and User:Slawekb? NE Ent 12:05, 26 December 2014 (UTC)

From the obvious box near the top of my user page "I typically operate an alternate account Slawekb because my name is long and the diacritics are not always available." Sławomir Biały (talk) 12:07, 26 December 2014 (UTC)

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## Thank you...

... for always taking the time to explain, like over at Talk:Spinor. Indeed, SO+(2, 1) is itself not doubly connected since its rotation subgroup is SO(2). That didn't cross my mind. I owe you a barnstar. (How active were you when you weren't semi-retired?) YohanN7 (talk) 18:28, 28 December 2014 (UTC)

We're all here to learn, after all.  :-) Sławomir Biały (talk) 18:57, 28 December 2014 (UTC)
It may take a few minutes from the time the email is sent for it to show up in your inbox. You can remove this notice at any time by removing the {{You've got mail}} or {{ygm}} template.
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## Thanks for the help

 The Reference Desk Barnstar Your reply at the math reference desk proved particularly helpful. Took me a couple days to work out the rest of the details, but ultimately it solved my problem. Thanks. Dragons flight (talk) 19:51, 31 January 2015 (UTC)

## help request for William C. Rader

Sławomir, I realize that you are semi-retired from Wikipedia (and that this historically contentious article may not be among your primary interests), but as a recently-registered user here I'm unable to edit/update with the news that Rader's medical license was revoked by the Medical Board of California in November 2014, after what appears to be a long investigation of his dubious stem cell marketing practices. I've provided the relevant link on Rader's talk page, with the hope that an established user like you will incorporate it into the article itself. Rader's loss of license has yet to receive significant media coverage but will no doubt prompt a sense of relief among legitimate stem cell researchers and scientists around the world. Thank you for your help Vesuvius Dogg (talk) 17:08, 28 February 2015 (UTC)

## Minor syntax fix

Sorry about disturbance - thanks for revert 650439127 and explanation. The actual problem is that formula has ambiguous syntax and does not render on some browsers. Not optimal esthetically, but maybe one of these is acceptable? ---Fakedeeps (talk) 13:24, 8 March 2015 (UTC)

${\displaystyle g_{\alpha {\overline {\beta }}}=g\left({\frac {\partial }{\partial z^{\alpha }}},{\frac {\partial }{\partial {\overline {{z}^{\beta }}}}}\right).}$
${\displaystyle g_{\alpha {\overline {\beta }}}=g\left({\frac {\partial }{\partial z^{\alpha }}},{\frac {\partial }{\partial {\overline {z}}^{\beta }}}\right).}$
Either one should be fine, and I have no objection to using one of these. But it seems most likely that the problem you are experiencing is a browser caching problem rather than something to do with the LaTeX itself. I could be wrong about that, but most likely I've found that if you see red text rather than the rendered equations this is the issue. Sławomir Biały (talk) 13:33, 8 March 2015 (UTC)
Is this about problems with "overline"? There is one such that seems to persist when using MathML. Don't remember the details (I did report it though to the relevant place (I think)), but nesting "overline" is at least hazardous. YohanN7 (talk) 14:12, 8 March 2015 (UTC)
Yes - overline. Error message says indexes are ambiguous: Error: "TeX parse error: Double subscripts: use braces to clarify". At some browser configurations it shows the red-text error, at others does not load; however commonly everything displays properly. Extra braces do fix the problem, but formula gets skewed/distorted a bit. I better leave it as is - agree that issue is elsewhere. Thanks for oversight. Fakedeeps (talk) 21:45, 8 March 2015 (UTC)

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## Another edit you might wish to revert

You might want to look at this, where similar logic is applied but more detail is given. I realize that it is OR and for that reason should not be included, but I am having difficulty pinpointing the error in the logic, so I thought I'd leave it to someone with clearer thinking. Uniqueness of an additive inverse should not a problem (we are assuming + is a group operation), I can see that the left distributivity law is implicitly used (but it is a given axiom), and there seems to be a proof that negation distributes. I see that a near-ring allows noncommutativity, but it simultaneously drops the left distributive property that was implicitly used and thus does not serve as a counterexample. I'm interested in seeing the flaw. —Quondum 19:11, 14 April 2015 (UTC)

I think he just proved that all groups are abelian. (The plus signs and the wording "additive inverse" etc, doesn't change the group axioms spelled out in items I-III one bit.) YohanN7 (talk) 20:13, 14 April 2015 (UTC)
I think the proof is right. The main lemma is the uniqueness of additive inverses. If ${\displaystyle x+a=a+x=0}$ and ${\displaystyle x+b=b+x=0}$, then ${\displaystyle b=b+0=b+(x+a)=(b+x)+a=0+a=a}$. (This proof uses that ${\displaystyle x}$ commutes with its inverse. Conversely, if we assume that right inverses are unique, then we can show that the right inverse is also the unique left inverse.)
Note that ${\displaystyle x+y+(-y+(-x))=0}$. By uniqueness of inverses, ${\displaystyle -y+(-x)=-(x+y)}$.
Now is where the ring axioms enter. For any x, we have ${\displaystyle (-1)x=-x}$. Indeed, ${\displaystyle 1x=x}$, so ${\displaystyle 1x+(-1)x=(1+(-1))x=0x=0}$. So, again invoking uniqueness of inverses gives ${\displaystyle (-1)x=-x}$. Hence on the one hand, ${\displaystyle (-1)(x+y)=-(x+y)=-y-x}$ (shown above). On the other hand, by the distributive law, ${\displaystyle (-1)(y+x)=(-1)y+(-1)x=-y-x}$ as well. So ${\displaystyle (-1)(x+y)=(-1)(y+x)}$, so multiplying both sides through by ${\displaystyle -1}$ gives ${\displaystyle x+y=y+x}$.
So, I don't object to including some statement later in the article about dropping commutativity from the hypotheses, but it should not be in the list of hypotheses for an abelian group. Rather it should be something like: "If we assume that ${\displaystyle (R,+)}$ is a group and ${\displaystyle (R,\cdot )}$ a monoid with identity satisfying a distributive law, then ${\displaystyle (R,+)}$ is automatically abelian." Also it needs a source if we say this. Sławomir Biały (talk) 11:51, 15 April 2015 (UTC)
But aren't items 1-3 in Q's diff [10], exactly the group axioms? YohanN7 (talk) 12:11, 15 April 2015 (UTC)
Ah, more is used than 1-3. Sry. YohanN7 (talk) 12:15, 15 April 2015 (UTC)
This might fall into the category of mathematical statements that cannot be challenged (i.e. there exists a straightforward, "obvious" proof), but would normally be skipped by authors, making it difficult to find a reference. Yet it is reasonable for someone to want to check this in a reference (WP?), because it is tricky enough to make people unsure. In such cases, the burden of finding a reference may be unnecessarily high. OTOH, I agree with S that the list of axioms is not the place to include it, even as a footnote. If it is mentioned, I would include it in a mention that several of the axioms are redundant; for example, equality of left- and right-sided inverses in a group is usually stated as an axiom, but is redundant (e.g. an associative loop is a sufficient definition). Redundant axioms seem to be quite common in the "usual" axiomatization of various structures. —Quondum 14:30, 15 April 2015 (UTC)
I don't think assuming the existence of a right inverse is enough to conclude the existence of a left inverse. For that, don't we need uniqueness as well? (Loops have uniqueness axioms for both inverses, don't they?) We could, for instance, start with a group G and look at words in G and a new variable k, modulo the relation xk=e for some x in G. It seems to me that an easy way around this whole question is to leave out the Hypothesis from ring that x commute with any right additive inverse. This is how it's done at vector space, and presumably it does lead to an independent set of axioms. Sławomir Biały (talk) 15:05, 15 April 2015 (UTC)
Agreed, existence of a left inverse does not imply existence of a right inverse. My illustration using a loop is poor, because it already has redundancy in its axioms. Rather use the statement in Quasigroup: "An associative quasigroup is either empty or is a group". An associative quasigroup axiomatizes no identity element or inverses; only associativity and left and right division (i.e. existence and uniqueness for each left and right). The existence of an identity (if not empty), equality of left with right inverse, and commutativity of inverses are all theorems.
I guess it comes down to whether we want to state the axioms afresh (in which case we can choose to remove all redundant axioms, but which?), or build from other structures, in which case we allow redundancy. The latter allows simple, easily remembered definitions, such as "an abelian group under + and a monoid under ⋅, with ⋅ distributive over + on both sides". The point that the editor was presumably making is that we can drop the word "abelian", but I would argue that this would be confusing, nonstandard and only partially eliminating redundancy of axioms, despite being correct. I think the same argument applies to a vector space: use the standard definition as an abelian group with a field acting on it. Listing individual axioms should be an aid to the reader summarizing the inherited axioms, not the definition of the structure. —Quondum 16:53, 15 April 2015 (UTC)
While it may be interesting to try to find minimal axioms for everything, I think that a good definition should, if possible without too much redundancy, manifestly capture the essence of what it defines. Defining a group as a set with an associative binary operation with left inverses and left identity works, but is just silly, even unnatural. (These sufficient (seemingly) weaker conditions are probably rarely unique. For groups there are at least 4-5 of them giving a group structure.) YohanN7 (talk) 21:24, 15 April 2015 (UTC)

Lots of good points. I suppose it's best if we put one note on redundancy in each article. We probably shouldn't change the definitions, for, like YohanN7 said, independence is not necessarily the most important thing. The current dispute revolves around whether commutativity is redundant in a vector space, so I left a large proof of that on the relevant talk page. Once everyone agrees that it works, we can move on and decide how to note that in the article. Also, a note, as proved there, a right inverse IS actually always a left inverse, and, obviously then, vice versa, in any sort of semigroup where every element has a right inverse. That's an essential result for all this dependence of axioms stuff. The short version is, if x + y = 0, then y + x = y + x + y + z, where we suppose z to be a right inverse of y, and that's then y + 0 + z = y + z = 0, so a right inverse is a left inverse. In other words, elements summing to 0 commute. David815 (talk) 22:07, 23 April 2015 (UTC)

## A kitten for you!

Aw, but I love it when people claim to have solved Millennium Prize problems!

PureRED (talk) 14:01, 21 May 2015 (UTC)

I kan haz million?

## That "mathematical conjectures are solved" guy

I don't pretend to understand higher math & conjectures & proofs but found this review of Prastaro's work here to be useful to my layman's mind: https://mixedmath.wordpress.com/2012/08/24/reviewing-goldbach/ as well as this column: http://www.scottaaronson.com/blog/?p=304. Thank you for wading into that particular AN/I discussion, I appreciate your expertise. Shearonink (talk) 17:11, 4 June 2015 (UTC)

Thanks for your comment at ANI in which you pass along your own investigation. To avoid any misunderstanding, and given the difficulty of proving conscious deception, it would be better if you remove the word 'fraud' from your post. Also the idea of writing to journal editors (sensible though it might be) contains the idea of off-wiki consequences, which might be viewed as having a chilling effect on another person in the WP discussion. Thanks, EdJohnston (talk) 18:38, 4 June 2015 (UTC)
I leave it to the kitten-and-bunny brigade, if they think self-obsessed crackpots should be nurtured as valuable to our project. I don't really see that as a constructive use of my own energies. Surely the whole point of bringing up one's own crackpottery in public fora like this is to bring it to wider attention. I'm fully entitled to bring this to the attention if the editorial board of Mathematical Analysis and its Applications. This is a basic right of any scientist. The only "chilling effecy" I see is you telling me not to be a part of peer review because something happened "on wiki". Sławomir Biały (talk) 20:33, 4 June 2015 (UTC)

Dear Professor Krantz,

My name is Slawomir Bialy. I am a regular mathematics editor on the English language Wikipedia. I am writing to express concern over the editorial standards of the "Journal of Mathematical Analysis and Applications" on whose editorial board you serve. I would specifically like to ask: (1) what is the policy of the editorial board on the retraction of papers? (2) what is the editorial policy regarding claims to have solved longstanding conjectures (e.g., Millennium problems)? (3) does the editorial board stand behind the integrity and quality of papers published in the aforementioned journal?

This inquest relates specifically to a recent case involving someone claiming to have settled the well-known Navier-Stokes existence and smoothness in an article published in the aforementioned journal (MR2386488):

Prástaro, Agostino Geometry of PDE's. IV. Navier-Stokes equation and integral bordism groups. (English summary) J. Math. Anal. Appl. 338 (2008), no. 2, 1140–1151.

This article makes a number of claims that should have flagged it for special editorial review. In particular, it claims to characterize existence and smoothness of global solutions of the Navier-Stokes equations. In fact, the author of this paper further affirms at the following Wikipedia "talk" page to have "completely solved" the Navier-Stokes problem in this paper:

https://en.wikipedia.org/w/index.php?title=Talk:Navier%E2%80%93Stokes_existence_and_smoothness&oldid=562819747#NS_Existence_and_Smoothness:_An_Algebraic_Topologic_Proof

This same author has, on the Arxiv and elsewhere, claimed to have applied similar "integral bordism" methods to solve a number of outstanding problems in mathematics, such as the Goldbach conjecture, Landau's problems, the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, and the smooth Poincare conjecture.

While the quality of his work on the Navier-Stokes equation is difficult for me to judge, the basic pattern in this author's contributions is rather clear: create an elaborate enough formalism to conceal the fact that nothing of substance is actually being done. This suggests a deliberate act of fraudulent research, violating basic principles of academic integrity.

I am deeply concerned that the journal has not done due diligence in investigating the quality of this purported research, and as such is negligent (if not complicit) in what seems to be a violation of basic principles. Since you are a world-renowned and respected academic, I am certain you will give this matter your full attention.

Best regards,

Slawomir Bialy, PhD Wikipeida

## Profession?

I have questions, one weak and one strong. First, do you have a PhD in Mathematics? Second, do you focus on editing articles relating to STEM? That way I can ask you questions regarding mathematical articles on Wikipedia, if you consent. Thank you. Dandtiks69 (talk) 06:16, 8 June 2015 (UTC).

## edit by user:isambard kingdom

yo slaw,

check out tensor, isambard added the SAME source he tried to insert in vector space

thoughts?

~~ — Preceding unsigned comment added by 174.3.213.121 (talk) 19:33, 9 June 2015 (UTC)

## Semi-Riemannian manifolds

Hi Sławomir,

haven't heard back from you on this point. I'm curious what you were referring to when you said semi-Riemannian manifolds were metric spaces and didn't have metric tensors. It's been a long time, but I'm pretty confident that I learned the term as synonymous with what you are calling pseudo-Riemannian manifolds, and I haven't been able to find any reference to the notion you cite as semi-Riemannian manifolds. --Trovatore (talk) 03:40, 28 June 2015 (UTC)

## Decent function?

Hi there, Sławomir. I noticed that you were the editor who wrote the first version of the Radial function article, in which you used the expression "decent function". Can you clarify what "decent" means in this context? Thanks, Waldir talk 12:30, 14 July 2015 (UTC)

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Hello, I'm Pigsonthewing. I wanted to let you know that your signature ("sig") design might cause problems for some readers. This is because the drop shadow. If you think I made a mistake, or if you have any questions, you can leave me a message on my talk page, or take a look at our guidelines and policy on customising signatures. Thank you. Andy Mabbett (Pigsonthewing); Talk to Andy; Andy's edits 11:23, 27 July 2015 (UTC)

The policy you pointed to does not mention drop shadows. Many editors have drop shadows in their signatures. I have for about six years now. They are not forbidden by any policy or guideline. The tutorial referred to at WP:SIGAPP has several examples of signatures with drop shadows, for example. If the issue is that you personally have trouble with custom signatures, there are instructions at WP:SIGAPP on how to override them. Sławomir Biały (talk) 12:07, 27 July 2015 (UTC)
The policy I pointed to is headed "Make sure that your signature is easily readable and does not cause disruption to other editors" It then continues: "Your signature must not... cause inconvenience to or annoy other editors." (emboldening in original). You appear to labour under the erroneous belief that it only concerns the specific examples that it then lists. Andy Mabbett (Pigsonthewing); Talk to Andy; Andy's edits 12:57, 27 July 2015 (UTC)
As far as I can tell, only one of us is causing inconvenience and annoying other editors. I find your request disrespectful and rude. If you believe that I have violated policy, go ahead and indefinitely block me. I have no intention of changing my signature, given such a combative and disrespectful request. You're just being a bully, and that is absolutely not acceptable behavior. Sławomir Biały (talk) 14:03, 27 July 2015 (UTC)

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'Consequently works better in the context here.' - please argue why this should be the case. --Mathmensch (talk) 11:47, 12 August 2015 (UTC)

Two reasons. First, and most obviously, it is not the case that "its decimal representation never ends and never settles into a permanent repeating pattern" is equivalent to the statement "π cannot be expressed exactly as a common fraction, although fractions such as 22/7 and other rational numbers are commonly used to approximate π." Indeed, numbers with non-terminating decimals are not "commonly" approximated by "fractions such as 22/7". However, it is true that having a non-repeating decimal does follow from the irrationality of π, so "consequently" would seem to be the correct logical connective. The fallacy in using "equivalently" is that the first sentence is two independent clauses, only one of which is equivalent to the conclusion.
The second reason has to do with the overall structure of the first three sentences of the paragraph: "A is true. Consequently, B. Because B, C might be true." It is a chain of modal implications. I think adding an unnecessary equivalence to that chain is not clarifying, especially when the last sentence is not a strict implication (the normality of π only might be true). 12:11, 12 August 2015 (UTC)
OK, point registered. What about the following version?
Being an irrational number, π cannot be expressed exactly as a common fraction. Equivalently, its decimal representation never ends and never settles into a permanent repeating pattern. Still, fractions such as 22/7 and other rational numbers are commonly used to approximate π. The digits appear to be randomly distributed; however, to date, no proof of this has been discovered. Also, π is a transcendental number – a number that is not the root of any non-zero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.
I would prefer at least a slight change as indicated above since the equivalence is an interesting fact and would enrich the article IMO. --Mathmensch (talk) 13:20, 12 August 2015 (UTC)
Or perhaps even better:
Since π is an irrational number, the decimal representation of π never ends and never settles into a permanent repeating pattern. Equivalently, π cannot be expressed exactly as a common fraction. Still, fractions such as 22/7 and other rational numbers are commonly used to approximate π. The digits appear to be randomly distributed; however, to date, no proof of this has been discovered. Also, π is a transcendental number – a number that is not the root of any non-zero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.
--Mathmensch (talk) 13:29, 12 August 2015 (UTC)
The first revision is an improvement. I don't like the second alternative as much, because it reverses the logical order (an irrational number by definition is a number that cannot be expressed as a fraction), and also does not segue into the next sentence. I would support the first proposed text. 14:35, 12 August 2015 (UTC)
On a slight side note here, I wonder if "common fraction" is really the best choice of words. It's not a very common expression, at least in the US, and some readers may interpret it as "proper fraction" (a fraction where the numerator is less than the denominator). Note that the link is not particularly helpful. Can't we say "ratio of integers" instead? --Trovatore (talk) 17:38, 12 August 2015 (UTC)
Slight update: Hmm, sometimes the link goes to the right section, sometimes not. Don't know why. Maybe an issue with my local browser setup or something. Still, we shouldn't rely on links to make the text clear. I am not convinced "common fraction" is in wide use, and would prefer the unambiguous "ratio of integers". For that matter, I think even just "fraction" would be an improvement, without the "common". --Trovatore (talk) 17:58, 12 August 2015 (UTC)
Perhaps the following third proposal meets all criteria:
Being an irrational number, π cannot be expressed exactly as a fraction (equivalently, its decimal representation never ends and never settles into a permanent repeating pattern). Still, fractions such as 22/7 and other rational numbers are commonly used to approximate π. The digits appear to be randomly distributed; however, to date, no proof of this has been discovered. Also, π is a transcendental number – a number that is not the root of any non-zero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.
--Mathmensch (talk) 18:39, 12 August 2015 (UTC)
I think the "equivalently" part should be a separate sentence, as it appears in the first revision above, since the digits of π are emphasized later. 18:47, 12 August 2015 (UTC)
But then the 'Still, ...' sentence seems to refer to the "equivalently" part. --Mathmensch (talk) 21:57, 20 August 2015 (UTC)

## Convenient vector space

Why put the calculus template at the end of the article? That's weird. Lbertolotti (talk) 19:14, 8 September 2015 (UTC)

Thanks. The template doesn't really make much sense for the article, whatever its placement. I've removed it. 19:49, 8 September 2015 (UTC)

## I have invited additional eyeballs to the talkpage, to peruse my own behavior

My apologies for the template, per WP:DONTTEMPLATETHEREGULARS.

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## Scriptstyle

You say \scriptstyle is for subscripts and superscripts, not inline maths. I'm not aware of this guideline. Could you point it out? If you ask me, the regular [itex], being so large, looks hideous inline. Jimp 09:07, 8 November 2015 (UTC)

Scriptstyle does not render correctly in the various automatic conversions employed by Wikimedia software. In particular, the mathjax extension, which we hope one day to be made the default for all users, will not render correctly in mathjax. Many users have the rendering method set to generate PNG images. On desktop interfaces, these can appear larger than the surrounding text. But on mobile interfaces, they appear smaller, and scriptstyle is almost indecipherable. 16:21, 8 November 2015 (UTC)
Fair enough but it would be nice if something could be done, ay? Jimp 10:54, 12 November 2015 (UTC)
It's been time to get math working for a very long while, but unfortunately it isn't a priority for the devs (who are volunteers), and the WMF just wants to throw money at useless things like visual editor, media viewer, and flow. There have been reams of discussion about this at WT:WPM. 11:18, 12 November 2015 (UTC)
Inefficiency at Wikipedia; what's new? Jimp 01:53, 13 November 2015 (UTC)
I'd say (Pig)TeX is not for inline math at all as things stand. Appearance is random. The randomizing factors are individual settings and hardware. I personally "display" more equations than I'd do normally, and use HTML math templates for the remaining inline math in the articles I care about. YohanN7 (talk) 10:50, 13 November 2015 (UTC)
Indeed, with the rise of mobile I can confidently say that math rendering has actually gotten worse for this very reason. Once upon a time, the default was for the server at least to try to render displayed math as html. But that was removed with the promise of mathjax support. For a time, mathjax was around, but now it's been removed. At this point, MathML actually looks pretty good. I'm guessing it's not the default yet because of lack of universal support of MathML. But hopefully that will change in time. 11:02, 13 November 2015 (UTC)
Yes, MathML looks decent on my setup too (big screen), even inline. I switch between PNG and MathML because of the bugs/missing features in MathML. YohanN7 (talk) 11:07, 13 November 2015 (UTC)

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## November 2015

Please stop your disruptive editing, as you did at Wikipedia:Identifying reliable sources. Your edits have been or will be reverted or removed.

Do not continue to make edits that appear disruptive until the dispute is resolved through consensus. Continuing to edit disruptively may result in your being blocked from editing. --Guy Macon (talk) 01:46, 19 November 2015 (UTC)

In my opinion after carefully examining the article talk page, the edit that I re-instated is fully supported by consensus and your edits are not. This should be obvious to you from all of the comments disagreeing with you.
I am sorry to hear that you think that threats of blocks don't seem likely to lead to constructive progress. That leaves me with the choice of letting you change a guideline against consensus or seeking to have you blocked. I have chosen the latter. Further discussion on this should be at ANI, where an uninvolved administrator will decide what to do about this situation. See notice below. --Guy Macon (talk) 03:10, 19 November 2015 (UTC)
Guy, this is still not a clear explanation of your position on that edit. The issue seems to be that the added content did not faithfully capture what is in WP:MEDRS. So, I have now included a direct quotation from that guideline. (The passage in question has been a part of that guideline since at least 2011.) There does seem to be support on the talk page that standards of science journalism have slipped, and that many news sources no longer engage in fact checking. This appears to be especially true of science journalism. So, there seems to be broad agreement on that. I think we could even get agreement that news sources are fine as primary sources, but not secondary sources. It already says as much at WP:MEDRS, and this was the thrust of my more substantial edit that you reverted. I'm sorry that you are unwilling to engage substantively on this issue. 03:18, 19 November 2015 (UTC)
Not going to discuss there here. ANI is over that way. Unwatching this page. --Guy Macon (talk) 06:17, 19 November 2015 (UTC)

There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. The thread is User:Slawekb / User:Sławomir Biały keeps changing Wikipedia:Identifying reliable sources without consensus. Thank you. Guy Macon (talk) 02:24, 19 November 2015 (UTC)

Isn't Wikipedia wonderfully democratic? Here every crackpot can drag you to the jury for anything they chose, using authoritative language. They seek opportunities to do it and love it. They love "rules" more than anything else. It isn't particularly important what the rules actually say, but the important thing is that there are "rules" that someone may break. That said, of course, Guy might not be one of those, don't know. YohanN7 (talk) 11:54, 19 November 2015 (UTC)

## ArbCom elections are now open!

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## ArbCom elections are now open!

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## ArbCom elections are now open!

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## Formula test

Hi User:Slawekb,

One of the new devs is working on an expanded LaTeX-based tool in VisualEditor. Would you mind helping her with some testing work? I want to give her the benefit of hearing from a couple of editors who aren't very familiar with VisualEditor. All you need to do is to click here: http://en.wikipedia.beta.wmflabs.org/wiki/Equation?veaction=edit and see if you can figure out how to change a formula that's there and/or add a new one. I'm specifically interested in your thoughts about the formula editor. If you want to see the current version of the math tool, then you can click here to edit my sandbox on the English Wikipedia. VisualEditor in general isn't difficult to use; it basically works like a typical word processor.

You can leave feedback at WP:VEF (about anything, including the formula tool), and feedback specifically about the formula tool directly at the dev's talk page at mw:User talk:TChan (WMF), or in phab:T118616 and related tasks, if you'd rather post directly to Phab. You can also reply on my talk page, and I'll forward it. Thanks for considering my request. Whatamidoing (WMF) (talk) 19:20, 2 December 2015 (UTC)

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## Exponentiation and Commutative Groups

You wrote: "Please don't change inline latex into html. See WP:MOSMATH"

Don't you mean don't change inline HTML into LaTeX? I call your attention to [11]

"both are acceptable and widely used ... One should not change formatting boldly from LaTeX to HTML, nor from non-LaTeX to LaTeX without a clear improvement. Proposed changes should generally be discussed on the talk page of the article before implementation."

Perhaps this is worthy of discussion on the Exponentiation article talk page. I see a clear improvement versus the clumsy inline HTML of the embedded sequences of exponents in this instance.

As for exponentiation "sometimes" being commutative, that indeed is the point being corrected with my edit. Exponentiation is sometimes commutative, which is the essence of the special cases in which it does in fact form commutative groups, or in the general case where a large exponent is factored. The commutative law of multiplication applies to the exponents when exponentiation is factored, but only to the order in which the exponentiation is performed not in terms of the base and exponents changing places, which is why Diffie-Hellman key exchange works. Are you willing to consider an edit to make my contribution more clear, or do you insist that nothing at all about exponentiation ever possesses a commutative property? RiskNerd (talk) 05:09, 2 January 2016 (UTC)

Yes, I meant don't change html to latex. Latex is not a good choice for very simple inline formulae. I disagree that exponentiation is commutative. Commutativity would mean that ${\displaystyle b^{a}=a^{b}}$. This is not true in the situation of a "commutative group" (for example, take a and b to be positive real numbers; that's a commutative group, but exponentiation is not commutative). What is true is that (a^b)^c = (a^c)^b. But that's not the same thing as commutativity of a binary operation. 12:17, 2 January 2016 (UTC)

## Delta Epsilon Iota

I'm interested in "Completing" to at least stub level the Greek Letter Organizations that are part of the Professional Fraternity Association. One of those is Delta Epsilon Iota. Since you are the editor who did started the Wikipedia:Articles for deletion/Delta Epsilon Iota, I'd like to see if I can create a stub that would be appropriate. I'm a fairly experienced editor who is a member of Wikipedia:WikiProject Fraternities and Sororities.Naraht (talk) 18:44, 17 January 2016 (UTC)

If Delta Epsilon Iota is a member of the Professional Fraternity Association, and that is considered a sufficient condition for notability, then a brief and neutral stub is acceptable. I would recommend watching the article for COI. The deleted version was much more than a stub, and was sourced entirely to promotional material and press releases. We were unable to find any independent reliable sources on the subject, and the article had been exclusively edited by COI editors. Obviously, such sources would be highly desirable if the article is recreated. 12:29, 18 January 2016 (UTC)

## Annabelle (Doll) page

Hey, I just put in a request for comment about the "legend" section. I didn't even know there was deleted content that covered it, until after I put it in. However I still think my version covered the section sufficiently better than the original did and was more clear about the dubious nature of it. I would ask that maybe you could look over the section again and chime in. I feel that you might of saw the content reapear and just of had a knee jerk reaction against it but I do feel it is an improvement over the old one. Regardless, I'll wait and see what the consensus says about it. --Deathawk (talk) 05:42, 15 February 2016 (UTC)

## Hilbert spaces

In this edit you wrote "I think a rather enlightening perspective is that in quantum mechanics it isn't really the Hilbert space itself that one sees, but rather its dual."

If you have time, would you very kindly be willing to expand a little on that, or perhaps give me a reference for it?Chjoaygame (talk) 04:42, 25 February 2016 (UTC)

The point I was making there was that, while elements of ${\displaystyle L^{2}}$ are usually thought of as "functions", that isn't really true. One needs to identify two measurable functions if they are equal almost everywhere. In quantum mechanics, this isn't necessary because all measurements that can be made rely on the dual space. That is, whenever we get a number out of a quantum measurement, we are in some way invoking the duality between bras and kets. But the dual of the space of square integrable functions is already a Hilbert space, so there is no need to identify things that are equal almost everywhere. It happens for free. 16:10, 25 February 2016 (UTC)
Thank you for that helpful commentary. If you have a little more time, would you perhaps give a reference for it, if such is to be found? I already have Dirac 1926:
In order to be able to get results comparable with experiment from our theory, we must have some way of representing q-numbers by means of c-numbers, so that we can compare these c-numbers with experimental values.<Proc. Roy. Soc. A, 110: 561–579.>
and Messiah on page 247 of volume 1:
In order to introduce a metric in the vector space we have just defined, we make the hypothesis that there exists a one-to-one correspondence between the vectors of this space and those of the dual space. Bra and ket thus associated by this one-to-one correspondence are said to be conjugates of each other and are labelled by the same letter (or the same indices). Thus the bra conjugate to the ket |u is represented by the symbol u|.
One or two more would make it more secure.Chjoaygame (talk) 16:31, 25 February 2016 (UTC)
Chjoaygame, please don't even think about you trying to explain this in you-know-which-article. YohanN7 (talk) 14:05, 1 March 2016 (UTC)
The fact that elements of L2 are equivalence classes is contained in footnote #10. Already that is overkill to put in the main text. YohanN7 (talk) 14:52, 1 March 2016 (UTC)

## what d'you know

In May 2012 you told me (in WP:RD/Math, i guess)

For a course on matrices specifically, I would recommend Gilbert Strang's "Linear algebra and its applications", followed by Horne and Johnson's "Matrix analysis".

And now, unpacking some boxes with an eye to getting rid of excess books, I find that I somehow have a secondhand Strang. It must have been in a box since 2009 if not before. —Tamfang (talk) 07:04, 11 March 2016 (UTC)

responded to your post on incompleteness theorem..was trying to figure out how to alert you in case you wanted to respond again...I think I did it wrong, and just inserted your logo...so maybe go fix that if it's wrong and needs to be removed...but tried a bunch of things in the code...but nothing else I tried including the pinging template seemed to work... people seemed to be using Username: but that didn't seem to work....68.48.241.158 (talk) 20:18, 5 April 2016 (UTC)

## User:Slawekb

If you are going to use this user account to edit, could you not redirect that account's user pages to this account? It's very confusing for editors who might want to get in touch with you. Since this account has been inactive for over a year, I'm not sure if you are even reading this talk page. Liz Read! Talk! 21:27, 20 April 2016 (UTC)

I have already given good reasons for doing things this way. Please check see my user talk page, and the archives, thanks. The moniker "slawekb" is a familiar diminutive, which would not normally be acceptable to individuals just "want[ing] to get in touch with [me]". They should use my formal, official name Sławomir Biały. The sock account is because diacritics in my official account are harder to type on some terminals. I use primarily the Slawekb account because it seemed less confusing to use one account for my edits instead of two. If you would prefer that I jump around between the two accounts because you think two accounts is less confusing than one, that can be arranged. 00:02, 21 April 2016 (UTC)
And here is proof that the old account is still active. So we're done here, right? Sławomir Biały (talk) 00:41, 21 April 2016 (UTC)

## Your reversion of my contribution to tensors

You undid my revision. What was written before my edit was too general. The example was about a specific type of linear transformation, namely an endomorphic one. That is an important aspect because of the change of basis matrices which are used in the example. So now it is less accurate. If accuracy does not matter then we could also write 'function' instead of 'linear transformation' which is even more general. — Preceding unsigned comment added by Jadzia2341 (talkcontribs) 12:50, 21 April 2016 (UTC)

The word "endomorphic" is not in wide use (even in pure mathematics), so should be avoided here. You could say "endomorphism" (a word which is slightly more common), but many authors by "linear transformation" already mean a linear endomorphism, as we do here. That is clear from the context. 12:57, 21 April 2016 (UTC)

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## pi's edit

So I disagreed your revert,consensus is neither adding template nor making link in the text.And that's just your rule.And you are not semiretired.--Takahiro4 (talk) 16:48, 4 May 2016 (UTC)

See WP:BRD. Take it to Talk:Pi. 16:55, 4 May 2016 (UTC)
You,take it to Talk:Pi.--Takahiro4 (talk) 17:12, 4 May 2016 (UTC)

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## edit back and forth

do you honestly think in good faith that my improvement to your improvement isn't an improvement?? particularly the final sentence I added to the paragraph?? any "bias" would be stating "often" as "often" has a connotation other than "universal" or "almost always" etc etc which is inline with reality..do we really need to start a new talk page thread on this????68.48.241.158 (talk) 16:27, 6 May 2016 (UTC)

"Nearly universal" is just wrong. It implies that "area of a disk" is almost never used. Even a crude Google books search shows that this is not the case. Google scholar, for "area of the disk" versus "area of the circle" shows almost an equal number of uses. The Google books hits for "area of the circle" only outnumber those for "area of the disk" by a factor of 5. That's pretty clearly not as "universal" as you believe. 16:42, 6 May 2016 (UTC)
the helpful paragraph you added is about the very phenomenon that the phrase "area of a circle" is predominately used...the connotation of "often" here is something other than the phenomenon being discussed....I'm going to go at least put back in that final sentence I added and perhaps change "often" to something along the lines of "usually" or "most usually"....though I think the word "universally" is more accurate and more encyclopedic sounding...also, you shouldn't just do a blanket revert if there are improvements...but revert more specific things...If you want to revert this again, I'll start a talk thread, which is just going to be annoying to people but will be necessary if you insist on blocking improvements...68.48.241.158 (talk) 16:59, 6 May 2016 (UTC)
But it's not universal at all. That's just wrong. 17:29, 6 May 2016 (UTC)

## phrase

"Since curves of finite length have zero breadth.." is this accurate/best way of stating things?? does it imply curves of infinite length are somehow different? couldn't find anything via google along these lines...you tell me; I have no idea...68.48.241.158 (talk) 15:30, 7 May 2016 (UTC)

There exist nonrectifiable curves of nonzero 2-dimensional Lebesgue measure. 15:35, 7 May 2016 (UTC)
does this somehow have to do with finite vs infinite as the phrase suggests?? again, I have no idea...the phrase seems jarring to someone not highly advanced to this technical degree (ie me)..68.48.241.158 (talk) 15:38, 7 May 2016 (UTC)
Yes, curves with infinite length can have positive area. 15:42, 7 May 2016 (UTC)
okay, I'll take your word for it..I can't personally imagine how an infinite length can affect the breadth of a curved line...68.48.241.158 (talk) 15:55, 7 May 2016 (UTC)
I asked a question about this looking for an intuitive explanation on the reference desk, simply out of my own personal curiousity...I quote from your statements but don't name you...in case you want to/have the time to make an attempt at explaining....68.48.241.158 (talk) 16:23, 7 May 2016 (UTC)
https://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Mathematics#how_can_lines.2Fcurves_of_infinite_length_have_positive_area.3F — Preceding unsigned comment added by 68.48.241.158 (talk) 16:24, 7 May 2016 (UTC)

Paul Adamson The Processionist (talk) 00:08, 12 May 2016 (UTC)== Just a thank you. ==

Your depiction of the spinor helped me to correlate a phenomenon, in my physics model, with the standard model. This correlation will end up being part of my description of the xion particle, which gets its name from the modification of the Lorentz contraction, by the inclusion of the Xi variable (The LorentzXi contraction.) So, thank you. :D — Preceding unsigned comment added by 67.53.34.76 (talk) 23:56, 11 May 2016 (UTC)

I'm glad you found it stimulating. Sławomir Biały (talk) 00:12, 12 May 2016 (UTC)

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## Relativity spaces

I apologize for failing to notice your response at WP:RD/Math for several days; I had checked back after a while, and then was distracted. Given that the thread has been archived, I'm not sure where best to respond. Briefly, I'm interested in finding a simple geometric intuition that I can use to explain a geometric visualization of Galilean relativity, special relativity and then hopefully the closely related de Sitter and anti-de Sitter alternatives to a young person. My tendency is to explore a larger class of related objects to seek broadly applicable ideas, hence a brief exploration into complex numbers. Feel free to move this as you feel appropriate. —Quondum 05:54, 3 June 2016 (UTC)

Hi there. Did you accidentally revert the wrong edit? The quaternion book published by Birkhäuser doesn't sound as if it's fringe. Did you mean the bioinformatics reference instead? Martijn Meijering (talk) 10:53, 21 June 2016 (UTC)

@Mmeijeri: It seems very dubious in light of this edit by the same editor. Sławomir Biały (talk) 11:09, 21 June 2016 (UTC)
Ah, I see. Martijn Meijering (talk) 11:42, 21 June 2016 (UTC)

## primes/recurrence relation

Hi,

I added a comment to the talk page re your deletion of the example of a recursively defined function listing all the primes (not only a subset, as the published and referenced example does). Isn't there a theorem in logic that says this had to be possible anyway because primes are a such-and-such set (recursive, recursively enumerable, primitive recursive or whatever the correct def'n is) and a suitable reference? I'm probably not going to go further with this, but it is strange having a published example that lists a subset of the primes when anyone can write down a similar example which lists them all in the correct order.Createangelos (talk) 12:11, 25 June 2016 (UTC)

OK, I just had a go myself, using an encyclopedia. The idea seems to be that any recursive set is recursively enumerable. A computer program to list them also can be encoded as a recursive function.Createangelos (talk) 13:03, 25 June 2016 (UTC)

## File:Belt trick 2.gif

Noting here I've just copied the upload history over to Commons, so the F8 tag can be reinstated.Jo-Jo Eumerus (talk, contributions) 22:38, 26 June 2016 (UTC)

## Continuum expression of the first law of thermodynamics

If you have sufficient knowledge to wriote an article on this subject, please feel free to do so, but the "article" that I replaced with a re-direct is not that article. Please do not revert the redirect again. BMK (talk) 00:34, 30 June 2016 (UTC)

## Fundamental problems with Wikipedia

Thanks for your recent edits on Infinite monkey theorem.

I read your userpage quotes with interest. You'll probably appreciate the essay on my userpage, especially the conclusion. ··gracefool 💬 06:40, 5 August 2016 (UTC)