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'''Reductio ad absurdum''', also called [[proof]] by contradiction, is a method of mathematical proof.  It involves assuming the opposite of what one is trying to prove, and showing that this would lead to a contradiction. It works by the law of the excluded middle. The proof typically follows this structure:

'''Reductio ad absurdum''', also called '''proof by contradiction''', is a method of [[mathematical proof]].  It involves assuming the opposite of what one is trying to [[prove]], and showing that this would lead to a [[contradiction]]. It works by the [[law of the excluded middle]]. The proof typically follows this structure:

#Create an initial assumption

#Create an initial assumption

#Therefore the initial assumption is incorrect

#Therefore the initial assumption is incorrect

An example of this is [[Euclid]]'s proof of the infinitude of the [[Prime number|primes]]:

An example of this is [[Euclid]]'s proof of the [[infinitude]] of the [[Prime number|primes]]:

#Assume there are finitely many primes

#Assume there are finitely many primes