Talk:Exponential Dominates Polynomial


 * $\displaystyle \sum_{m \geq 0}\frac{(\alpha n)^m}{m!} > \frac{(\alpha n)^{k+1}}{(k+1)!}$

Why? --GFauxPas (talk) 19:48, 9 July 2013 (UTC)


 * Because the the latter is a summand of the former when $m=k+1$ --Ybab321 (talk) 00:05, 18 October 2013 (UTC)

Real polynomials
It seems the proof would be identical for the growth of polynomials in $\R$, am I wrong? If so, should I copy - paste - find-and-replace this theorem into Exponential Dominates Real Polynomial ? --GFauxPas (talk) 15:14, 15 November 2016 (EST)


 * Meh. I'd rather this (appallingly carelessly imprecisely stated) proof was made to apply to all reals than another proof written. Using Archimedean principle, for any $x \in \R$ there is an $n \in \N$ such that $n > x$ and the job is done.


 * But the answer is always: go to your source works rather than trying to craft stuff out of whole cloth -- at this level of mathematics there is no research left to be done, and a "new" proof or a "new" result will either already be out there somewhere or (worse) just not be any good. --prime mover (talk) 15:47, 15 November 2016 (EST)