Oh, so you're good at calculus anon? Can you find the derivative

>>7992740
give me the function and i'll find it BITCH

Analysis is the anal sex of mathematics, it feels great when stuff works, but if you're not careful you get covered in shit and diseases.

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>>7992767
>he doesn't immediately recognize the weierstrass function

>>7992767
>being this new

>>7992787
no

Even in calculu, undergrads learn many functions are not diferentiable and probably someone will mention wierstras in there. You are a second second semester undergard feeling superior for knowledge you cannot justify. Consider killing yourself faggot.

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>>7992740
I like fucky graphs

>>7993091
>mfw mention to my friend who is a sophmore mech engineer about the weierstrass function one day
>he didn't know that continuous nondifferentiable functions could be things

ahh to learn real analysis for the first time. i bet you guys are all finally feeling like real mathematicians.

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>>7993157
Fuck thuis gay world

>>7993157
Did you before reading the Weisterass function Wikipedia page?

>>7993184
It's not that complicated, but you should know how "strong" a postulate should be.

>>7992787
yes

>>7993184
yes.

>>7993184
>he didn't recognize abs(x) is a trivial example

what kind of shit calculus program did you go through

>>7995750
There's a difference between being differentiable everywhere except one point (a "sharp corner" as is usually described in into calculus) and being nowhere-differentiable (something which is not that trivial to construct or imagine).

>>7995797
That is true. But if you understand mathematics at all, you should realize from the fact that there are functions that are continuous but not differentiable at a point, that there could well be functions that behave that way in more general forms, until proven otherwise.

Easy. It's average derivative is 0, otherwise it's not self similar.

>>7993007
It says it on the picture

>>7995821
Really? I always thought it was a remarkable and not at all obvious fact that you can form differentiable nowhere functions.

>>7995945
It's not obvious at all.

Their construction heavily relies on the completeness of [math]R[/math] and of [math] C([0,1], R) [/math]. You can do it by hand with rescaled series (that's how you build Weierstrass function or Takagi function), but using Baire theorem you can prove that in fact, continuous functions who are nowhere differentiable are dense in the space of continuous functions.

And with the natural gaussian probability measure on [math] C([0,1], R) [/math], they're also of full measure : if you take a random continuous function it will always be nowhere differentiable. That's one property that makes Brownin motion so interesting

>>7995945
They are not easy to construct but, in a sense, "most" continuous functions are differentiable nowhere.
As a general heuristic rule of thumb, you should keep in mind that any sort of order is exceptional (most functions are not continuous, integrable, etc. most continuous functions are nowhere differentiable, most numbers are irrational, most numbers are transcendental...)