> I wouldn't go as far as calling it a bad idea but I do consider it a style error when a a proof by contradiction is used even though a proof by contraposition

> I wouldn't go as far as calling it a bad idea but I do consider it a style error when a a proof by contradiction is used even though a proof by contraposition would do. A common style of proof among novice mathematicians, and even occasionally some professionals, is the good old: "Let's prove `P` by contradiction. Assume `not P`. Then [direct proof of `P`]. Therefore, we have a contradiction." (I think that the fondness for this technique above all others among novices is that, no matter how hard the problem, you always at least know how to start a proof by contradiction.)