What is a proof by contradiction? A proof by contradiction is if is true.
One assumes that a proposition P is False, and uses that to derive until a contradiction is reached, which can’t be True.
A popular example: Let’s prove that is irrational. An irrational number is something that cannot be expanded into a fraction. (A common misconception is that Pi is and therefore rational; no it is not exactly .
See http://mathworld.wolfram.com/PiFormulas.html
Assume that is rational; such that we can represent it as , where is a fraction in lowest terms.
If both and are even, they are not in lowest terms, as both can be divided by 2 for further simplification. Hence we have a contradiction.