Talk:Euler's Number is Irrational

Hey, anyone know how to align the eqns used here? I tried but I couldn't make it work. If so, feel free to tidy up this page. :)

Thanks either way, -Dan

Hey, I think the best way so far to do that would be to use a table. Matt Westwood uses tables here, it looks nice and seems to work well. --Joe 00:08, 13 August 2008 (UTC)

Thanks! I love his format and it makes this a lot more readable. Thanks again.

Also, might want to further specify the subcategories (number theory is a big place!) and maybe consider adding a category for proofs of irrationality. They're sort of my favorite, so I'd fill it right away. Would it be possible to show subcategories (e.g. Proofs of Irrationality) and also each individual proof (the way you do it now) on the same Number Theory page, a la Wikipedia? -Dan

Any use can add categories, all you have to do is add that category as you would any category, then follow the red link for that category, to its page, then assign that category page to either the main Proofs category, or another subcategory. Hope that made sense, if not let me know --Joe 04:27, 13 August 2008 (UTC)

Would it possible to add a step showing that $m(n - 1)! - (n! + n! + \frac{n!}{2!} + \ldots + \frac{n!}{n!}) \geq 1$? You say that it is "composed entirely of sums of integral components and is equal to a sum of positive terms,", but that's not clear to me. I see that $(n! + n! + \frac{n!}{2!} + \ldots + \frac{n!}{n!}) = (n - 1)!n(\sum_{i=0}^{n}\frac{1}{i!}) < (n - 1)!ne = (n - 1)!m$, but that just shows it is greater than 0, not 1 as required by the proof. - Josh

I should also mention I think this is a really great proof! Good job! - Josh

RickettsAM pointed out to me that $m(n - 1)!$ and $(n! + n! + \frac{n!}{2!} + \ldots + \frac{n!}{n!})$ must be integers and so must their difference; but I think those steps should be added to the proof. - Josh

Better? I added a line clarifying why it must be > 0. Is it still unclear? I try to avoid spoon-feeding each realization to the reader, but I feel like the page does most of the work for you.

If I have some time soon, I'll add/fill categories and update a lot of the titles that need it. (They seem to need some kind of standard; I'll work on it.) -Dan

I find it more clear now - I thought before your references to sums were somewhat ambiguous, whereas now you indicate more clearly what you mean. I don't think this is a case of asking to be spoon-fed, I just interpreted a line differently than you intended it; if I known what you meant I would have simply asked you to rewrite that one line as you did. --Josh 23:16, 13 August 2008 (UTC)

Not sure $e$ has ever been called "Euler's constant". I thought that was $\gamma$ otherwise known as the "Euler-Mascheroni constant" and defined as $\lim_{n \to \infty} \sum_{k=1}^n \frac 1 k - \ln n$.

So I renamed it in the text.--Matt Westwood 05:38, 14 August 2008 (UTC)