A Christmas Theorem

by Fish-Face at 8:01 p.m. on 22. December, 2013

Theorem. Santa Claus exists.

Proof. Let S be the sentence "If S then Santa Claus exists." This looks a bit self-referential but actually such a sentence, or an equivalent one, is constructible by the Diagonalisation Lemma.

Now, S is of the form P\implies Q where P (the antecedent) is just S and Q (the consequent) is "Santa Claus exists." So of course if we assume P and show that Q is true, then we have showed P\implies Q. Hence assume S. Hence (by S) Santa Claus exists. But this was the consequent. Hence S. Hence Santa Claus exists. \qed

Corollary. Merry Christmas!

Related tags: christmas humour maths theorem


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