math ppl:
my prof said that "for now" fₓᵧ=fᵧₓ. Anybody know what kind of functions these could be unequal for? terms to google would be cool but ELI5 would be even better. I can't even imagine at this point
, any ideas?
Conversation
the problem is that the partial derivatives might not be continuous and then things can get wacky:
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Ok discontinuity is not so wacky*, happens at a point bc of divinding by 0 or whatever. I was worried they were somehow two different functions across the whole domain and it was messing me up inside
I am sure it can get wacky af in some circumstances
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Hey there it is! I knew she used a weird word and I was trying to remember so I could google it
"pathological"
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Ironically, "pathological" functions are much (much, much) more common than "well-behaved" functions
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As in they come up frequently in deceivmbing the world or "more of them exist, abstractly"?
Or perhaps more likely, something else entirely?
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abstractly mostly, although sometimes the world too, e.g. brownian motion
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ok brownian motion wiki page officially puts over my math threshold for the day, wtf is going on
thanks for playing everyone
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it’s the continuous limit of a random walk if that helps