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? --ʀ6ʍɑʏ89 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#Equivalence of characterizations 1 and 3, 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. --ʀ6ʍɑʏ89 01:21, 5 February 2006 (UTC)