User talk:D.Lazard

Definition of the real number power

I define integer power as:

$a^{n}=a\cdot \quad \dots \quad \cdot a\quad (n\,{\textrm {times}})$

Now I want to define real number power via logarithms:

$a^{r}=e^{r\cdot ln(a)},\quad r\in R$

I can calculate $x=r\cdot ln(a)$, but the resulting x is again a real number, so I still don't know how to calculate $e^{x}$. You said the way of defining exp(x) —using integer powers— does not matter here. Thus far I can calculate integer power and rational power. How do I calculate $e^{x}$ according to the alternative definition? ale (talk) 11:30, 15 February 2019 (UTC)

To editor Ale2006: The alternative definition supposes the knowledge of the exponential function and the natural logarithm, and is better written as

$a^{r}=\exp(r\ln a).$

If one puts a = e in this formula, one gets

$e^{r}=\exp(r),$

if one knows that $\ln e=1.$ This explains why $e^{x}$ is commonly used for denoting $\exp(x).$

So, the alternative definition does not depend of any exponentiation, and this is why I wrote "the way of defining exp(x) does not matter here". The definition of the exponential function in terms of a power series is fine, but I do not like it, as it involves the non-elementary concept of convergence of a series, and does not explains the choice of particular coefficients. This is the reason for which I prefer to define the exponential as the unique function that equals its derivative and takes the value 1 for $x=0,$ and the natural logarithm as the antiderivative of $1/x$ that takes the value 0 for $x=1.$ Either of these two functions is inverse of the other because of the differentiation rule for inverse functions. As e is defined as $\exp(1),$ this shows $\ln e=1.$

Above considerations may be summarized as follow: For giving a definition, it is always useful to examine the other definitions that are hidden behind the used terminology. This is fundamental for avoiding circular definitions and for avoiding definitions that are unnecessary complicated or technical. D.Lazard (talk) 12:24, 15 February 2019 (UTC)

The current text only says that The natural logarithm ln(x) is the inverse of the exponential function. That defines the logarithm, not the exponential. If it were a definition of exp(x), it would have spelled The exponential function exp(x) is the inverse of the natural logarithm. That would indeed be circular, since most definitions of the natural logarithm suppose the knowledge of the exponential function.

Supposing the knowledge of exp(x) to define real number power sound circular to me, unless you somehow recall that exp(x) can be defined without knowing real number power. You preferred definition of exp(x) via derivatives is good, but it also implies the convergence of a Taylor series. And anyway it is missing from that subsection either... Heck! Right now I noticed that the previous subsection gives a definition of exp(x) in terms of a limit of integer powers. I hadn't seen it yesterday. That's why the definition seemed circular to me.

Perhaps, the convergence of a limit is easier than that of a power series? Let me try recalling it. If you still dislike my edit revert it again and I won't try any more times. Just try to read that paragraph ignoring the previous one. ale (talk) 17:39, 15 February 2019 (UTC)

rogue bot?

Hello,

As I understand it, your javascript bot undid the edit I happened to make yesterday on Angle trisection

I strongly suggest you give your bot some insights on mathematics, semantics and image analysis so that it doesn't invalidate valuable information such as the one I posted.

Please _read_ and _analyze_ personally (that means don't let the bot do the job) the content of the paper posted on wikimedia commons _before_ you (or your bot) decide to invalidate modifications on this article.

Once the proof I have provided has been validated by mathematicians of international reputation (which, by providing the paper on wikimedia commons, was a way of providing these mathematicians the opportunity to view and validate my proof), your bot will look foolish. Since you're the one operating the bot, it seems obvious you will by then have made a total fool of yourself.

I have once already been faced with a wikipedia "moderator" (or should I say "censor") that tried to revert some first-hand information I gave about swiss electrical outlets. He finally changed his mind. I sure hope what now seems a standard "you plebs have no authority to edit wikipedia" will quickly come back to a true, collaborative encyclopedia.

Regards. — Preceding unsigned comment added by Petaflot (talk • contribs) 20:40, 20 February 2019 (UTC)

To editor Petaflot: I am not a bot, and I do not use any bot. I assume to have reverted you edit, because it does not follows any Wikipedia rule. Firstly, Wikipedia does not accept any original research (see WP:OR), and your edit is blatant original research. Secondly, every possibly controversial or disputed assertion must be supported by reliable source (see WP:Reliable sources), and your source is clearly not reliable, as not regularly published, and not supported by any secondary source (see WP:SECONDARY). Finally, as your result contradicts a well know and well studied theorem dated from 1837, if your result would be true, this would logically imply that all modern mathematics would be wrong.

So your edit cannot be accepted without breaking the main policies of Wikipedia. D.Lazard (talk) 21:22, 20 February 2019 (UTC)

Angle trisection

Hello,

thank you for your answer ; somehow I got two different ones and that confuses me.

I have, in the mean time, sent my papers to "real" mathematicians and have already started debating the validity of the procedure.

I feel flattered that you see this as original research ; I don't believe it is because it's only the application of a known algorithm to a known problem.

You may, however, also be aware that Gallileo's work was considered to be correct until Newton came along, whose work was also considered to be correct until a guy who went by the name of Einstein proved him wrong. In the meantime, generations of mathematicians and physicists blindly accepted what eventually turned out to be flawed proofs. In fact, I don't really care if _you_ believe or not that Wanzel (and others) could be wrong : the method works and that's a fact, measurable _and_ computable.

In a short time I shall also provide an explanation of how and why George Cantor was mislead when he stated his "diagonal" theory. That theory, in particular, is one of the biggest frauds I'm aware of in the history of mathematics. I'm also aware this will definitely not please the majority of mathematicians who have built an extensive system on flaky grounds and will need to reconsider quite a lot of the things they believe they have proven on top of this fraudulent theory : it's actually gonna hurt way more than proving Wanzel was wrong. Shit happens.

Wikipedia is not a place for "religious" considerations dictated by a small elite that has a clear interest in the conservation of their monopoly of "truth". It is a place for people to share their knowledge. In this regard, this edit was clearly _not_ an act of vandalism.

If you are not a "competent mathematician" as you say, then it should not be _your_ decision to edit a post such as mine to purely and simply suppress that information ; instead, you should make sure such mathematicians have access the subject so they can give prove or disprove it, and at the very most edit the page in such a way that it would say something like "An amateur mathematician based in La Chaux-de-Fonds believes he's formalized a method to trisect the angle with straight-edge and compass but this has not yet been cross-proved nor dissmissed".

Additionally, the method I propose solely uses a straight-edge and compass ; this fits the antique definition of the problem (which says nothing about not using recursive procedures) and hence should be considered as valid. I hereby invite you to try this method on any scale and see for yourself if it works. : if you do it right, I guarantee it will.

Comment

You left a comment on my talk page: "I have the (possibly wrong) impression that you are not yet fully aware of the Wikipedia guidelines on this subject". I was wondering what gave you that impression. Thanks. Latex-yow (talk) 22:22, 25 February 2019 (UTC)

To editor Latex-yow: Normally, discussions should not be split into several talk page. This is why I answer here with a template insuring notification, instead replying on your talk page,

Sorry, my post was caused by an edit by another user, who changed ℤ into $\mathbb {Z}$ instead of ℤ, including in a section header. My error come from several of your edits, such as this one where you have changed many (not all) formulas, sometimes reduced to a single letter, from html to latex. Apparently, your most recent edits follow the guidelines that I have tried to summarize, so my post was probably not useful, and you may ignore it. D.Lazard (talk) 10:46, 27 February 2019 (UTC)

Thanks for responding. With respect to the edit you link to, I changed ƒ to LaTeX because that character should not be used per guidelines, while f and f have readability and spacing issues. I switched C to $\mathbb {C}$ because the article also used both and I was aiming for a uniform notation. When an article uses a consistent notation for $\mathbb {N} ,\mathbb {Z} ,\mathbb {Q} ,\mathbb {R} ,\mathbb {C}$ I don't convert it, say, from \mathbb to \mathbf. Finally in LaTeX formulas "\ldots" is preferable to "...". Latex-yow (talk) 11:24, 27 February 2019 (UTC)

Edit of the infobox of Paul Erdős

Hello, you reverted my edit for as you said, because I didn't summarize, I consider my goal is not only to summarize but also to unify as much information as possible on the main page with the associated pages, but also to keep it comprehensive, i.e. "summarized". As far as my conception of "known for" is concerned, I don't have a narrow minded approach towards the concept of 'known for" that I presume you have, a mathematically ignorant person may or may not "know" a person or his name because of his direct "contributions" to knowledge.

Also, to back up my argument, I'll also mention you 3 few "good","protected" and a "featured" article that have the same format of representation of "known for" field that I tried to edit in my editing of Paul Erdős' article.
Please have a look at the following articles: Richard Feynman, John von Neumann and Paul Dirac. The 3 aforementioned articles are rated "featured, "good" and "semi-protected" respectively also have a lengthy collapsible list.

Also, to avoid a super-lengthy infobox, I added a collapsible list, as it'd hence, be intuitively understandable to the reader that the associated field may contain a long/medium sized information.

My request to you would be not to revert the article and to allow my previous edit, as it'll both unify and summarize the article's infobox.