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Pulling out an inductive proof by contradiction, along with an obscure (to me) formula, is impressive for someone who doesn't do proofs on a regular basis :)
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Proof by contradiction was my favorite method in college. I think it's easier because you know where to start and you just move forward. So even to prove that things are true, I'd just assume the converse and show a contradiction.
Because a non-contradiction based proof seems harder. You know where you want to go, but you don't know where to start.
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Yeah, Reductio ad Absurdum were also my favorites.
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Nice. Are you a mathematician, @Scroogey?