In the classic proof of irrationality of SQRT(2) we assume that it can be represented by a rational number,a/b where a, b are integers. This assumption after a few mathematical steps leads to a contradiction, namely that both a, b are even numbers. Why is that a contradiction? Well you can say that the rational fraction has to be in its lowest terms;therefore either a or b or both must be odd. However, that wasn't in the assumption(lowest terms). The assumption was just two integers a,b. Why can't they both be even?