Re: Irrationality of e^k
- From: israel@xxxxxxxxxxx (Robert Israel)
- Date: 21 Apr 2005 06:33:39 GMT
In article <GmD9e.38561$qO6.37464@trnddc05>,
Hans Engler <h.engler@xxxxxxxxxxx> wrote:
>Does anybody know an "elementary" proof that e^k is irrational for all
>integers k? By "elementary" I mean a proof that uses facts like the
>differential equation or functional equation for the exponential function,
>the Maclaurin series for e^x and ln(1+x), or possibly the limit formula lim
>(1+x/n)^n = e^x.
This is a special case of the elementary proof that e is transcendental,
given e.g. in Herstein, Topics in Algebra, Theorem 5.F. This proof uses
nothing more advanced than the mean value theorem.
Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
- References:
- Irrationality of e^k
- From: Hans Engler
- Irrationality of e^k
- Prev by Date: Re: Group GL(2,3)
- Next by Date: Re: JSH: Objectivity, linking hyperbolas
- Previous by thread: Irrationality of e^k
- Next by thread: Re: Irrationality of e^k
- Index(es):
Relevant Pages
|
