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
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
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