Let's prove that there are two irrational numbers, call them \(a\) and \(b\), such that \(a^b\) is a rational number! And let's do it in a tweet.

Twitter proof:

β Mathspp (@mathsppblog) July 23, 2020

Let a=b=β2. If a^b is rational then there is nothing to be done. Assume a^b is irrational. Redefine a=β2^β2. Notice how a^b = (β2^β2)^β2 = (β2)^2 = 2 which is clearly rational. QED.https://t.co/3sFinyzJwu

Do you have an idea for a twitter proof? Let me know in the comments below!

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