Talk:Proof of e as a limit

I think that the proof should remain on Wikipedia as it does not really fit under Characterizations of e. The proof of e as a limit is not already included in Characterizations of e and it is an important proof so I think it belongs on its own page. Blotwell, were you suggesting a merge between the articles or that we just eliminate the proof altogether? -- ʀ6ʍ ɑ  ʏ89  14:50, 4 February 2006 (UTC)
 * It's a proof of the same statement as already proved in the section Characterizations of the exponential function, except that the one already there is more general because it proves $$\lim_{n\to\infty}\bigg(1+{x\over n}\bigg)^n=e^x$$ for any x whereas you only proved the case $$x=1$$. Also that page is much more clear about what definition of e you're starting from, which is important:  if your definition of e was $$\lim_{n\to\infty}\bigg(1+{1\over n}\bigg)$$ then the "e is this limit" theorem would be obvious:  but you would instead have to prove that the derivative of $$\log_e x$$ was $$1/x$$.
 * If you think that this proof could be better described and signposted then I agree. I'd certainly be in favour of changing e (mathematical constant) to make it clearer where to find the proofs.  But please work with (or point out problems with) the existing pages rather than creating duplicates.  —Blotwell 00:32, 5 February 2006 (UTC)
 * OK. I understand where you're coming from; thanks for clearing that up. -- ʀ6ʍ  ɑ  ʏ89  01:21, 5 February 2006 (UTC)