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:— Mathspp (@mathsppblog) July 23, 2020
Let a=b=√2. If a^b is rational then there is nothing to be done. Assume a^b is irrational. Redefine a=√2^√2. Notice how a^b = (√2^√2)^√2 = (√2)^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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