Talk:e (mathematical constant)

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Most people do not realize that x^(1/n) is the nth root of x, those same people having been affected by the stuck neuronal bit named root off, which makes it more difficult to see the inverse of the mathematical relationship in multiplication f(x)f(1/x)=1.

In math & science, those affects are related to theological & social pretext issues, where a demand is made to be consistant with social theology, but not with math nor science. Lot´s of social theological terms & issues in math and the sciences, the largest one, being an insistance on immortality through demanding that individuals memorize names, as if that would re-incarnate those same individuals.

The truth of that manner? It does, but solely parcially so. ;-) — Preceding unsigned comment added by 190.79.47.80 (talk) 13:57, 4 August 2013 (UTC)

Note: Kindly remove if/when not/no longer applicable <statement added by originator of the comment>. — Preceding unsigned comment added by 190.79.47.80 (talk) 11:51, 5 August 2013 (UTC)

An interchangeable concept, a competitive example to pi

pi is as trivial as the circumference of an unit circle, one doesn't need to evaluate pi in terms of infinite decimals to speak of the application of pi. One can think of the circumference of an unit circle inplace of pi, whenever he/she sees pi. Personally, compound interest still can't satisfy me. e still lacks such (geometric) intuition (maybe that's why it is taught only since highschool). Even so, i still believe that e is as mathematically beautiful and as trivial as pi. We just haven't explore enough. --14.198.222.131 (talk) 15:51, 21 September 2013 (UTC)

Intuitive explanation

Since my edits have been overridden please see my take at it, in my user space at User:Pashute\E (mathematical constant) IMHO its a more intuitive explanation and more clear for the layman, and beginning student, whereas in the current way its written it is not immediately clear what the meaning of e is, and why it is important. In any case, the basis for my edit was of course the great work done till now. (I just added e to it). פשוט pashute ♫ (talk) 12:53, 4 October 2013 (UTC)

The proposed edit completely disregards the manual of style recommendations set forth at WP:LEAD. The lead is supposed to define the topic of the article and to summarize the contents of the article, and thus provide a capsule version of the article. Moreover, the explanation involving plant stems offered in the edit seems to be completely wrong. At any rate, even if it could be corrected, such an explanation requires a source. Since the standard explanation of continuous growth in most sources is that of continuously compound interest, obviously this should carry more weight than a rather marginal explanation involving plant growth. WP:WEIGHT would decide the extent to which the latter even belongs in the article. Finally, the formulas
$e = \sum_{n=1}^\infty \left(1+\frac{1}{n}\right)^n$
$e = (1+\frac{1}{1}) + (1+\frac{1}{2})^2 + \cdots+(1+\frac{1}{n})^n$
added in the proposed revision are both obviously incorrect. Sławomir Biały (talk) 13:19, 4 October 2013 (UTC)
I agree with Sławomir Biały's restoration. I'm afraid your changes have many serious problems, with layout, formatting and unusual language. This is a good article, and as such does not need radical overhaul, or have problems with clarity or meaning. --JohnBlackburnewordsdeeds 13:31, 4 October 2013 (UTC)
A technical comment: while I’m a bit surprised that the system allowed you to do it in the first place, note that the page you created is a user page of a nonexistent user “Pashute\E (mathematical constant)”. A subpage of your own user page, which is apparently what you intended, would be User:Pashute/E (mathematical constant), with a normal slash. Please mind this in the future.—Emil J. 13:41, 4 October 2013 (UTC)
I've moved it to its proper location; there's now a redirect at User:Pashute\E (mathematical constant) which will hopefully be deleted.--JohnBlackburnewordsdeeds 13:47, 4 October 2013 (UTC)
Thank you for moving it. Nothing to do with plant stems. Everything to do with completely missing the point of e.
Here's what Kalid from BetterExplained.com had to say about the current type of explanation: (my emphasis)
"...What does it really mean? ... Math books and even my beloved Wikipedia describe e using obtuse jargon... Nice circular reference there... I’m not picking on Wikipedia — many math explanations are dry and formal in their quest for “rigor”. But this doesn’t help beginners trying to get a handle on a subject (and we were all a beginner at one point) ... Describing e as “a constant approximately 2.71828…” is like calling pi “an irrational number, approximately equal to 3.1415…”. Sure, it’s true, but you completely missed the point... Pi is the ratio between circumference and diameter shared by all circles. It is a fundamental ratio inherent in all circles ... e is the base rate of growth shared by all continually growing processes. e lets you take a simple growth rate (where all change happens at the end of the year) and find the impact of compound, continuous growth... e shows up whenever systems grow exponentially and continuously: population, radioactive decay, interest calculations."
He concludes: (with his original emphasis)
"So e is not an obscure, seemingly random number. e represents the idea that all continually growing systems are scaled versions of a common rate.
And then goes on to explain what continual growth is. I think my explanation is clear and good. I'll add more sources to what I wrote. I also will add a better and more intuitive explanation about e in calculus and the natural logarithm. That is the other part. I'll put my edits currently Under Construction, and when done, will ask you, my fellow wikipedians to have your say. Thank you פשוט pashute ♫ (talk) 11:53, 7 October 2013 (UTC)
Whoever wrote that apparently didn't read the article past the first sentence. The definition involving the natural logarithm is not circular, as mentioned later in the first paragraph and in detail later in the article. The article does discuss the role of e in continuous growth, with a mention in the first paragraph, and in-depth treatment in the Applications section. Sławomir Biały (talk) 11:28, 8 October 2013 (UTC)

source code examples

Should there be a example program that calculates Euler's constant? I added a C program but it was reverted.

This is the program that i was intending to add:

#include <stdio.h>

long factorial(int n) {
long result = 1;
for (int i = 1; i <= n; ++i)
result *= i;
return result;
}

int main ()
{
double n=0;
int i;
for (i=0; i<=32; i++) {
n=(1.0/factorial(i))+n;
}
printf("%.32f\n", n);
}

Please tell me if this is a beneficial addition. Thea10 (talk) 21:33, 19 October 2013 (UTC)

I don't think it should be included. Wikipedia articles generally do not include source code except in articles about programming languages and closely connected topics. Sometimes, in the case of notable algorithms, it's acceptable to include pseudocode. But in this case the code snippet is just a transcription of the series definition of e, so a pseudocode implementation seems redundant at best. Sławomir Biały (talk) 19:52, 20 October 2013 (UTC)
What about adding a link to the source code in the "external links" section?, There is a link to the many digits of e, I think that the source code would be more beneficial. Thea10 (talk) 20:22, 20 October 2013 (UTC)
If you're planning on linking to an implementation, then it should be a high quality implementation. The C code above is very poor. It performs no checks to see if the double n has the requested number of digits, which is presumably potentially an issue depending on the precise implementation of C and the processor that the code is run on, Anyway, there are clearly going to be underflows all over the place. If you're coding it in C, then you'd better do it properly: this is what multiprecision libraries are for. Sławomir Biały (talk) 20:49, 20 October 2013 (UTC)
(Actually, it's worse than simple underflow. The factorial function will give an integer overflow at some point midway through the program. Sławomir Biały (talk) 13:22, 21 October 2013 (UTC))
Even a high quality implementation is little more than a programming exercise, and tells you nothing interesting about the constant. Apart from of course the digits but they are already in the article (to 50 places) and linked. So there would be no value to such a link.--JohnBlackburnewordsdeeds 21:11, 20 October 2013 (UTC)

e in calculus

$\frac{d}{dx}a^x=.....=a^x\left(\lim_{h\to 0}\frac{a^h-1}{h}\right).$ When the base is e, this limit is equal to one.

No proof is given, but it appears that the limit, which is the slope of $f(x) = a^x\,$-1 at x=0, is equal to 1 is because the definition of e is s.t. $\frac{d}{dx}e^x = e^x$. This then becomes a circular definition to use the definition $\frac{d}{dx}e^x = e^x$ to derive the conclusion that $\frac{d}{dx}e^x = e^x.$. Mezafo (talk) 04:54, 28 October 2013 (UTC)

One of several equivalent definitions of e is that it is the unique real number such that the derivative at $x=0$ of $e^x$ is equal to one. That is, e is the unique real number such that the value of the limit $\lim_{h\to 0}\frac{e^h-1}{h}$ is one. There's nothing circular about this definition. It is then used in the article to deduce that $\frac{d}{dx}e^x=e^x$. Sławomir Biały (talk) 14:28, 6 November 2013 (UTC)