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Wow I'm really surprised this didn't enter your post grad! We covered this briefly in undergrad but had a much meatier grad level course on fundamentals of computational with this included and it destroyed pretty much every student in the class lol. Our professor ended the final at 4 hours to "spare you the misery".

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hahaha okay actually in retrospect/closer inspection, I do think some teachers tried to instill these probability proofs from a different angle - though obviously it did not stick long past the testing, and I never thought of it as a fundamental new approach. Would definitely need to reformulate all of this into much more intuitive / visual metaphors to get it to really stick these days. Oddly I do a lot of thinking on the general fundamentals course content these days (FSAs, Turing Machines, etc) but I should really try to incorporate this probabilistic view

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