Re: prove it if you can

Proginoskes wrote: 
José Carlos Santos wrote:

[...]
Let _s_ be the square root of 2. I don't know whether s^s is rational or
not. If it is, then you're done. Otherwise, consider

   (s^s)^s = s^{s^2} = s^2 = 2.

So, if s^s is irrational, you have the example that you want. 
For the record, s^s is not only irrational, but transcendental. This is
a consequence of Lindemann's Theorem.


How so? All I know about Lindemann's Theorem is what I
googled for twenty seconds or so ago, and I can't see
how it implies that. The theorem tells us that if
a is algebraic, then exp(a) is transcendental. But
s^s is exp(ln(s)s), and surely ln(s)s isn't algebraic.

.