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Re: Does Mathematica think Sqrt[2] is rational?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg86681] Re: Does Mathematica think Sqrt[2] is rational?
*From*: magma <maderri2 at gmail.com>
*Date*: Tue, 18 Mar 2008 04:49:53 -0500 (EST)
*References*: <frkv66$109$1@smc.vnet.net>
Ops..
I have overlooked the trivial solution x=0 and y=0 in the logical
equation.
If we consider
Reduce[ForAll[{x, y}, x != 0 && Element[x | y, Integers], x^2 != 2
y^2]]
as suggested by Andrzej, Mathematica answers correctly.
Oh well.. the pythagoreans did not come back after all.
So Mathematica correctly realizes that Sqrt[2] is irrational.
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