Quote:
Originally Posted by chezlaw
I already edited.
Yes it would have taken me a while to realise you wanted me to go back to o level maths - Why you want it remains beyond me.
Here's a more fun one for you from day 1 of adult maths. By considering root(2)^(root2)^root(2) or otherwise, prove there exists irrational p,q such that p^q is rational
I'll put you out of your misery, since you obviously misremember the first day of adult maths. What you are referring to is a non-constructive proof that an irrational number can be raised to an algebraic power and produce a rational number.
The proof goes as follows: we stipulate rt(2) as irrational and algebraic. we raise rt(2) to rt(2). the result is either rational, in which case we are done, or it is irrational, in which case we raise it to rt(2) again, in which case we get 2, and we are done.
This proof is non-constructive as we don't know whether rt(2)^(rt(2) is rational. However, some time in the late 18th century, this number was proved to be transcendental (and therefore irrational) by the Lindemann–Weierstrass theorem.