structural:summarization, stylistic:style_transfer
Irrationality of the square root of 2

The classic proof that the square root of 2 is irrational is a refutation by contradiction. Indeed, we set out to prove the negation ¬ ∃ a, b ∈ N {\displaystyle \mathbb {N} }. a/b = √ 2 by assuming that there exist natural numbers a and b whose ratio is the square root of two, and derive a contradiction.