/sci/ - Science & Math » Thread #13782064

54KiB, 1080x510, Cantor Sex.jpg

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Cantor Set

Anonymous Sat 23 Oct 14:22:40 2021 No.13782064 View Reply Original Report

Quoted By: >>13782449 >>13782662 >>13782881

EXPLAIN THE CANTOR SET TO ME OR I'LL FUCKING KILL YOU! DON'T DUMB IT DOWN INTO SOME VAGUE SHIT! EXPLAIN THE CANTOR SET TO ME RIGHT NOW OR I'LL LITERALLY FUCKING KILL YOU! HOW THE FUCK IS IT UNCOUNTABLE? WHY THE FUCK IS EVERY POINT A LIMIT POINT? DON'T DUMB IT DOWN OR I'LL FUCKING KILL YOU!

Anonymous

View Same Google iqdb SauceNAO 17092794.jpg, 70KiB, 600x350

Anonymous Sat 23 Oct 2021 14:25:25 No.13782078 Report

Quoted By:

Anonymous

Anonymous Sat 23 Oct 2021 15:59:47 No.13782343 Report

Quoted By:

Cant

Anonymous

View Same Google iqdb SauceNAO IMG-20211018-WA0000.jpg, 40KiB, 845x651

Anonymous Sat 23 Oct 2021 16:05:23 No.13782356 Report

Quoted By:

Stop yelling.

Anonymous

View Same Google iqdb SauceNAO cant.jpg, 74KiB, 600x966

Anonymous Sat 23 Oct 2021 16:32:25 No.13782439 Report

Quoted By:

Anonymous

Anonymous Sat 23 Oct 2021 16:35:01 No.13782449 Report

Quoted By: >>13782501 >>13782575

>>13782064
The most fucked up thing about this set is that, although the number of elements is uncountably infinite, if you represent it in the way this image does, the number of lines will be countably infinite, despite there being more lines than actual points in the set

Anonymous

Anonymous Sat 23 Oct 2021 16:49:50 No.13782501 Report

Quoted By: >>13782573

>>13782449
That's not fucked up. Each line represents a choice between left or right. The picture just shows a countably infinite product of the set {0, 2} which is easily proven to be to be uncountable.

Anonymous

Anonymous Sat 23 Oct 2021 17:08:37 No.13782573 Report

Quoted By:

>>13782501
You are insane.

Anonymous

Anonymous Sat 23 Oct 2021 17:09:21 No.13782575 Report

Quoted By: >>13782598

>>13782449
every union of any number of lines will be uncountably infinite

Anonymous

Anonymous Sat 23 Oct 2021 17:17:03 No.13782598 Report

Quoted By: >>13782615

>>13782575
The number of lines in that pic is countable. Each level has a finite number of lines in it, and there are countably infinitely many levels. Thus the number of lines is a countable union of finite sets, which is at most countable.

Anonymous

Anonymous Sat 23 Oct 2021 17:23:53 No.13782615 Report

Quoted By:

>>13782598
yes and the union of the set of lines is uncountably infinite, as is the union of any set of lines

Anonymous

Anonymous Sat 23 Oct 2021 17:35:39 No.13782662 Report

Quoted By:

>>13782064
>HOW THE FUCK IS IT UNCOUNTABLE?
You're removing all numbers with a 1 in their ternary representation, so you end up with numbers that only have 0 or 2 in them, which easily biject with the unit interval using binary, which is uncountable.

>WHY THE FUCK IS EVERY POINT A LIMIT POINT?
Take any point x. Let a_n be the number in the Cantor set which matches up with x in the first n digits, then is different in the next one (replace 0 with 2 or 2 with 0), then agrees again. (a_n) is a sequence in the set, and converges to x, so x is a limit point.

Anonymous

Anonymous Sat 23 Oct 2021 18:44:55 No.13782881 Report

Quoted By:

>>13782064
it's the set of all real numbers whose ternary expansion includes only 0 and 2. both your questions are easy if you look at this way.

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