Re: exp(sqrt(2))

From: Daniel W. Johnson (panoptes_at_iquest.net)
Date: 09/01/04 

Date: Wed, 1 Sep 2004 14:52:01 -0500

Barnaby Finch <barnabyfinch@verizon.net> wrote:

> I believe I read that if x is algebraic (and not zero), then e^x is
> transcendental.

http://mathworld.wolfram.com/Lindemann-WeierstrassTheorem.html

> If e^x is algebraic (and not 1), then x is transcendental.
> I'm sure it's possible to choose a transcendental x such that e^x is also
> transcendental.

The set of real x such that either x or e^x is algebraic is obviously a
countable subset of the reals; this leaves the set of real x such that
neither x nor e^x is algebraic as uncountable. 

-- 
Daniel W. Johnson
panoptes@iquest.net
http://members.iquest.net/~panoptes/
039 53 36 N / 086 11 55 W

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