1. So is a Lemma is just a means to an end...? I didn't realize this. There is a proof that used a lemma to simplify the proof. Although there was an alternate way to solve the problem, the lemma made it a lot easier to follow and see what was happening. The alternate way was a fancy trick, but it was also one of those tricks that I never remember while I'm taking tests.
2. I am just loving all of these even/odd proofs. I can't imagine that they're going to go on forever, but I love them. So much beautiful algebra. It's pretty rewarding to get to the end of these proofs and see that you actually accomplished something. I think my most favorite thing about it is that you get the right answer, and then it's just a matter of proving your way there. I'm not too excited about having to decide if the proof is valid or not, because that's not the same as having the right answer and just having to figure out how to get there. Proofs are so much less evil these days. I love it.
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