Editing Proof by contradiction (section)

===Irrationality of the square root of 2===

The classic [[Square root of 2#Proof by infinite descent|proof that the square root of 2 is irrational]] is a refutation by contradiction.<ref>{{cite web|url=http://www.math.utah.edu/~pa/math/q1.html|title=Why is the square root of 2 irrational?|last=Alfeld|first=Peter|date=16 August 1996|work=Understanding Mathematics, a study guide|publisher=Department of Mathematics, University of Utah|access-date=6 February 2013}}</ref>
Indeed, we set out to prove the negation ''¬ ∃ a, b ∈ <math>\mathbb{N}</math> . a/b = {{sqrt|2}}'' by assuming that there exist natural numbers ''a'' and ''b'' whose ratio is the square root of two, and derive a contradiction.