I was surprised by the sample solutions that were posted recently for Problem Set 1. I had assumed that the proofs we were doing would follow the format from 165 (Assume, indent... then... then... assume, indent... then... then... dedent... then... dedent... then for all...). However, the sample solutions posted seemed much less formal than those from 165, and made much use of prose over symbols. I think I like the idea of writing a proof in paragraph form, given the difficulties I've been having with Assignment 1. In some ways, I've been having more problems expressing myself clearly than in actually understanding and finding a solution for the problems. My proofs to the first two questions look like someone spilled a bowl of alphabet soup on my monitor - way too many subscripts and variables. I think one of the reasons for that was that, if I wanted to discuss a subset of a certain set, without doing anything to the set itself, I would still have to declare and justify the existence of both, whereas if I were doing a more prosaic proof, I could describe the properties of the set and then move on to what interested me, only giving an explicit representation to the things that I was going to use.
If that makes sense.
I'm almost tempted to rewrite my proofs to the first two questions in the style of the sample solutions. I'm loath to erase the <100 lines I've already committed to them, though. I know I'll definitely be adopting a less formal technique for the last two questions, and the second problem set though.
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