Might be hard to sleep cause I didn’t leave my room today. It’s been a while since I left my room literally 0 times in a day. I didn’ t even go to eat
nya nya nya nya nya nya nya my real analysis homework is making me prove g(x) = x * sin(1/x); g(0) = 0 is continuous on [0, 1]
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proving it’s continuous at 0 is fine
proving it’s continuous everywhere else is proving to be very painful
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And you can’t even make it up. Because it’s a class for villagers
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I need to first prove that |sin(a) - sin(b)| <= |a - b| which will proooooooooobably be a rigorous enough proof but it’s not, like, amaaaaaaazing
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real analysis on the way to be about proving NOT INFINTESIMAL inequalities forever and ever and ever
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i told you epsilon delta over an interval sucks!
it’s not that tho
it’s normal epsilon delta with a bad function
…over an interval
nyaaaaa I mean
yes but I don’t need to choose one delta to match the whole interval
oh. well continuous functions on a closed and bounded interval are uniformly continuous so in theory you could
i’m getting you manganese for christmas
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nyaaaaaaaaaaa that’s real analysis tbthbthtbhtbtbthbthbt ← user was killed for this post
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also wait our real analysis class is doing this so philosophical style we haven’t even introduced trig functions yet
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when asked about it one day he said they’ll be defined as the limits of their taylor series, which like. sure.
how did you define exponentiation btw
oh i actually don’t remember
I’m so sad about the fucking payment method issue
probably as repeated multiplication somewhere down the line