Proof by contradiction versus proof by contraposition

This part of the paper explores the differences and similarities that exist between proof by contraposition and proof by contradiction. The literature refers to both methods as indirect methods of proof.

We now turn our attention to the other method, the proof by contradiction. As previously stated, in general, to prove a statement by contradiction, we assume that statement to be false and we show that the logical consequences of our assumptions lead to a contradiction or an impossibility.

A proof by contradiction assumes the following three propositions to be true.

Besides number theory proof by contradiction may be applied in many areas including geometry, linear algebra and calculus.