User talk:Sławomir Biały

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SEMI-RETIRED
This user is no longer very active on Wikipedia.

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

Taylor Series Exemple[edit]

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

\begin{align} \sum^\infty_{n=0} {x^{n+1}\over n!} =  \sum^\infty_{n=1} {x^{n}\over (n-1)!} \end{align}

My calculus will be

\begin{align} \sum^\infty_{n=0} {x^{n+1}\over n!} =  x + \sum^\infty_{n=1} {x^{n+1}\over n!} = x + x\sum^\infty_{n=1} {x^{n}\over n!} \end{align} and not the initial result.

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

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[edit]

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[edit]

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Talkback[edit]

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)

Examples of convolution[edit]

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[edit]

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:

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

Domain of definition[edit]

The convolution of two complex-valued functions on Rd

(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[edit]

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:

(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[edit]

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:

(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[edit]

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

(f * g)[n]\ \stackrel{\mathrm{def}}{=}\ \sum_{m=-\infty}^\infty f[m]\, g[n - m]
= \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[edit]

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[edit]

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[edit]

[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[edit]

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

Transpose: best abstract definition?[edit]

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)

about angle[edit]

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[edit]

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[edit]

Re your edit here http://en.wikipedia.org/w/index.php?title=Wikipedia_talk%3AWikiProject_Environment&diff=563829950&oldid=563780784

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[edit]

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 ?[edit]

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[edit]

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[edit]

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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[edit]

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

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 x^p is p x^{p-1}. This is identically zero for the field of p elements. But as a function 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 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 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 p field p^n. So derivatives of polynomials x^p and x just don't have any choice but to be different, despite the annoying fact that as functions x^p and x are indistinguishable over field 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 x and 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: x and 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 D^kf/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 D^kf/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)

AdS/CFT review[edit]

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[edit]

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?[edit]

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 e^{-(x^2+y^2)\epsilon} and then letting \epsilon\to 0. The integral
\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 \int_0^\infty e^{-\epsilon x^2}\cos(x^2)\,dx (likewise with sine) converge to the appropriate Fresnel integrals (in this case \int_0^\infty\cos(x^2)\,dx) as \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 \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[edit]

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[edit]

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)
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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[edit]

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[edit]

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.

for reference, https://en.wikipedia.org/w/index.php?title=Holomorphic_function&oldid=599710410&diff=prev

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[edit]

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[edit]

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Rational Pricing Discussion[edit]

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[edit]

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.

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A quickie[edit]

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[edit]

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[edit]

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

\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)

Disambiguation link notification for May 18[edit]

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Response: Beal's Conjecture[edit]

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[edit]

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[edit]

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 Face-smile.svg
Thanks for explaining about the bundle. YohanN7 (talk) 19:04, 6 July 2014 (UTC)