I like Jer's solution because it, albeit unintentionally, makes the case with the least to prove. If we know that sqrt(2) is irrational, then either sqrt(2)^sqrt(2) or (sqrt(2)^sqrt(2))^sqrt(2) must be an example, and it doesn't matter which.
eln x = x is the example I thought of, but it makes it necessary to prove that ln x is irrational for whatever rational x you choose.
The case for complex numbers involving i is addressed in my previous problem, "The Powers that Be.
** The square root sign is broken .. even when I manually add √ or √ in the "View Source" the box changes it to the ASCII character before submitting, which is then killed by the browser. That's not good ..
Edited on December 21, 2004, 1:58 pm
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Posted by DJ
on 2004-12-20 19:49:22 |
Weighing In
