reductio ad absurdum (idea)

Theorem proving technique that applies the modus tollens inference method. In practice,

1. you want to prove thesis A
2. you assume that A is false
3. you prove that the logical consequence of A being false is absurdity
4. you deduce that A is true

two favorite theorems proved by reductio ad absurdum (the latin phrase means "reduction to absurd") are:

• the square root of 2 is irrational, proved by assuming that square root of 2 is rational, and showing that that requires a certain number to be both even and odd at the same time.
• There is no largest prime number, proved by assuming that there is in fact such a number, and showing that you can always construct a bigger prime number. Contradiction results, although not as elegant as the previous one.