Re: PROVE sqrt(2)+sqrt(3) is a irrational number!!!

On Mon, 01 Oct 2007 12:04:07 -0700, Dave L. Renfro wrote:
G. Frege wrote (in part):

So let's consider (instead) the following claim:

1) a rational number which is not 0 times a irrational
number is a irrational number.

Here's something to play with.

We know an irrational number to an irrational power can be
rational. For instance, a^b is an example for a = b = sqrt(2)
or for a = sqrt(2)^sqrt(2) and b = sqrt(2).

False in the case of a = b = sqrt(2), by Gelfond-Schneider.

QUESTION: Can a^(b^c) be rational with a, b, c all irrational?

a = c = sqrt(2) and b = sqrt(2)^sqrt(2).



--
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case heard May 17
U.S. Court of Appeals, Third Circuit
<http://www.abu-jamal-news.com/>
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