Proof by contradiction

A variant of the syllogism gives rise to one of the most powerful techniques in mathematics: proof by contradiction.

Example — Syllogism by contradiction

“Every man is mortal” and “Zeus is immortal” $\implies$ “Zeus is not a man”.

This scheme is the basis of proof by contradiction: one assumes the negation of the thesis to be true and reaches a contradiction with the hypotheses. Since the contradiction is unacceptable, the negation of the thesis is false and therefore the thesis is true.

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Topics: Euclidean geometry
Concepts: Proof by contradiction · Syllogism
Skills: Proving