Proof_by_Contradiction

Definition

Wikipedia:

A proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Proof by contradiction is also known as indirect proof, proof by assuming the opposite, and reductio ad impossibile.

It usually proceeds as follows:

  1. The proposition to be proved, $P$, is assumed to be false. That is, $\neg P$ is true.

  2. It is then shown that $\neg P$ implies two mutually contradictory assertions, $Q$ and $\neg Q$.

  3. Since $Q$ and $\neg Q$ cannot both be true, the assumption that $P$ is false must be wrong, so $P$ must be true.

https://www.d.umn.edu/~jgallian/Proofs.html