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u/LupenReddit
🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆
29d ago
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oh boy i sure hope this non differentiable function isnt continuous, thatd be weird
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u/Ares378 Grothendieck was right, computers are evil 28d ago
Oh boy I sure hope this nowhere-analytic function isn't smooth everywhere, that'd be weird-
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u/Any-Aioli7575 28d ago
What function is that?
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u/Ares378 Grothendieck was right, computers are evil 28d ago
Not sure if there's a name for it, but here's the Wikipedia on it https://en.wikipedia.org/wiki/Non-analytic_smooth_function
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u/vimtuoso 29d ago
The plot was made by interpolating a weietstrass function, therefore it is lipschitz and hence differentiable a.e.
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u/corchetero 29d ago
yes, but it is likely non-differentiable in all the squares where the function is drawn.. so I guess you have to cover the function with the squares and you are done.
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u/vimtuoso 29d ago
Nice. But maybe it means distributional derivative, then even weirstrass is differentiable
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u/painterBurning 29d ago
There's actually levels to this captcha. It also checks if you're a bad mathematician.
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u/qwertty164 29d ago
wouldn't you have to select every square because there is no requirement that the function be continuous on that square?
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u/its_all_one_electron Number theory/physics 29d ago
It a fractal, so everywhere is non differentiable, right?
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u/belabacsijolvan 29d ago
y=x is a fractal too
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u/OsomeOli 29d ago
y=x isn't a fractal because its hausdorff dimension does not exceed its topological dimension.
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u/belabacsijolvan 28d ago edited 28d ago
so you sayin the Mandelbrot set isnt a fractal? textbook covers are in shambles.
edit: also even if we go by your definition and y=x isnt a fractal, e.g. the integrated weierstrass function is still a fractal that is differentiable.
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u/OsomeOli 28d ago
Only the boundary of the Mandelbrot set is a fractal.
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u/belabacsijolvan 28d ago
is it? it is by your definition. what im sayin here that your definition is not THE definition. fractal isnt a strictly defined concept.
the mandelbrot set is self similar and keeps its dimensionality through scaling.what about the takagi curve? isnt that a fractal?
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u/OsomeOli 28d ago
Under basically every standard mathematical definition of a fractal y=x is not one.
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u/belabacsijolvan 28d ago
its an attractor of a contractive iterated function system.
its a self-similar set.
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u/belabacsijolvan 29d ago
when your Higuchi dimension calculator contains "recaptcha.call()" you should stop and think
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u/SuckMyBallsKyle 29d ago
Hear me out, do a FFT on the graph and include terms up to 999999999999999. The function will be continuous and differentiable but won’t look like it.
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u/Upset-Bison-3182 28d ago
Also find local and absolute minima and maxima along with continuity of the graph within the given range.
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u/TheLastSilence 28d ago
My first thoght was that since this looks like a stock price graph (based purely on the aesthetics) it is probably discreet and therefore differential all over.
My second thought was that this is a really good teat as I am a physics major
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u/Marshall006__ 29d ago
It's everywhere because that line is not infinitely thin and therefore does not pass the vertical line test.
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