I'm in a proof class right now. We've covered direct proofs and moved on, but I'm still curious about them. Is there any important theorem that has even been derived using a direct proof (assume p to show q) or are they mainly just used to introduce proofs? In class, we only ever cover proofs such as "if n ##\equiv## 1 (mod 2), then n2 ##\equiv## 1 (mod 8)." and the like.
Sorry, I can't get the tex to work out... aha, just got it working, nevermind