Proof-that-2-2-R-Q-

Question Number 190480 by aba last updated on 03/Apr/23

Proof that {(\sqrt{2})}^{\sqrt{2}} \in R ∖ Q

Answered by mehdee42 last updated on 04/Apr/23

l e m : i f p \notin Q \Rightarrow \sqrt{p} \notin Q

c l i m : 2^{\sqrt{2}} \notin Q

p r o o f : i f 2^{\sqrt{2}} = \frac{p}{q} \in Q \Rightarrow p = 2^{\sqrt{2}} q

You can't use 'macro parameter character #' in math mode

\Rightarrow \sqrt{(2^{\sqrt{2}})} = {(\sqrt{2})}^{\sqrt{2}} \notin Q

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