indirect proof

In mathematics, a proof in which you assume temporarily that the conclusion is not true, and then deduce a contradiction.

For example:

Given: n is an integer and n^2 is even.

Prove: n is even.

Proof

Asume temporarily that n is not even. Then n is odd, and n^2 = n * n = odd * odd = odd. But this

contradicts the given information that n^2 is even. Therfore the temporary assumption that n is not

even must be false. It follows that n is even.

Indirect proofs, also known as reductiones ad absurdum (``reductions to the absurd'') are quite common in mathematics. In fact, students of mathematics tend to use them too often---providing an indirect proof where a direct one would do just as well.

Intuitionist mathematics (which is much more well-grounded than the name would seem to indicate; it is related to constructivism) does not allow the indirect method of mathematical proof.