/sci/ - Science & Math » Thread #13217274

15KiB, 1024x1024, Cantor Function.png

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Anonymous Mon 31 May 16:27:31 2021 No.13217274 View Reply Original Report

Quoted By: >>13217322

This is not continuous.
Don't care about your fancy math jargon to justify it. It's not continuous.

Anonymous

Anonymous Mon 31 May 2021 16:32:38 No.13217296 Report

Quoted By:

Continuous =/= Differentiable

Anonymous

Anonymous Mon 31 May 2021 16:36:30 No.13217322 Report

Quoted By: >>13217330 >>13217410

>>13217274
At which point is it not continuous?

Anonymous

Anonymous Mon 31 May 2021 16:38:18 No.13217330 Report

Quoted By:

>>13217322
Every point.

Anonymous

View Same Google iqdb SauceNAO 250px-Cantor_function_sequence.png, 26KiB, 250x266

Anonymous Mon 31 May 2021 16:41:00 No.13217341 Report

Quoted By: >>13217399 >>13217426

f_0 is continuous everywhere and differentiable everywhere
f_1 is continuous everywhere and differentiable at everywhere except for 2 points
f_2 is continuous everywhere and differentiable at everywhere except for 4 points
f_3 is continuous everywhere and differentiable at everywhere except for 2^3 points
f_n is continuous everywhere and differentiable at everywhere except for 2^n points

Anonymous

Anonymous Mon 31 May 2021 16:43:16 No.13217349 Report

Quoted By: >>13217369

What's with all the attacks on Cantor's work recently?

Anonymous

Anonymous Mon 31 May 2021 16:46:19 No.13217369 Report

Quoted By: >>13217389

>>13217349
Summer, so all the high-schoolers have nothing better to do.

Anonymous

Anonymous Mon 31 May 2021 16:49:36 No.13217389 Report

Quoted By:

>>13217369
They haven't had much to do for quite some time since last year, thanks to all the school breaks they had during lockdown.

Anonymous

Anonymous Mon 31 May 2021 16:53:22 No.13217399 Report

Quoted By:

>>13217341
-the graph is composed of straight segments that have 0 slope
-the graph is somehow monotone
therefore, none of the segments are continuously connected.

Anonymous

Anonymous Mon 31 May 2021 16:55:50 No.13217410 Report

Quoted By:

>>13217322
This is like asking "what's the next real number after 0?". It doesn't mean anything.

Anonymous

Anonymous Mon 31 May 2021 16:58:34 No.13217426 Report

Quoted By: >>13217459

>>13217341
Congratulations, you've correctly shown that for finite n, the function is continuous. How do you expect to prove that also applies to n=infinity?

Anonymous

Anonymous Mon 31 May 2021 17:05:50 No.13217459 Report

Quoted By:

>>13217426

Because Its uniformly convergent because after the nth iteration the function is within 1/2^n of the final value at all points.

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