/sci/ - Science & Math

>>8943967
Here's the Weierstrass function, which is continuous everywhere but differentiable nowhere.

Hello /sci/,

we all know there are continuous but non differentiable. And we even know they form a dense subset for the [math] ||.||_{ \infty} [/math] norm.

But what I want to know is a little more tricky : is there a continous and differentiable function [math] f [/math] but with [math] f' [/math] continous nowhere ?

>>8164661
0/10 shitpost. See me after class.

Oh, so you're good at calculus anon? Can you find the derivative of this function for me please? What, you can't? You must not be very good then!

What are some of the most surprising mathematical facts or theorems you know?

Pic related.

>>7235090
You're welcome

>>7139484

l2weierstrass

<div class="math"> \sum_{i=0}^{\infty} a^n \cos (b^n \pi x) </div>
<div class="math"> 0 < a < 1, b </div> is a positive odd integer
<div class="math"> ab > 1+ \frac{3}{2} \pi </div>

now simply quit bein a bitch
and generalize that shit using analytic continuation to all complex numbers

>>6370190
Weierstrass function

She's continuous everywhere, but differentiable nowhere.

>>6089592

>what's your favorite curve?

Not a curve, but pic related. It's the graph of the Weierstrass function, which I think was the first explicit function that is continuous everywhere but nowhere differentiable, illustrating a key regularity (or lack of regularity) property to early analysis folks.