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/sci/ - Science & Math

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7441779 No.7441779 [Reply] [Original]

thoughts on the Banach-Tarski Paradox?
how would you be able to explain this

>> No.7441795

examples of when this could happen in the real world?

>> No.7441805

>>7441779
>>7441795
>real world
ha

I interpret it as being similar to "the cardinality of the evens is equal to the cardinality of the odds is equal to the cardinality of the positive integers"

>> No.7441817

>>7441779
stop watching vsauce

>> No.7441820

>>7441805
Except you'll be surprised to hear that Banach-Tarski doesn't work for the unit disc. Suddenly it doesn't look like it has anything to do with just infinite cardinalities...

>> No.7441826

FUCK OFF VSAUCE-WATCHING REDDITOR

>> No.7441841

>>7441779
I was waiting for B-T to become a pop math meme tbh
I saw this coming

>> No.7441864

>>7441779
Weird shit happens when you deal with infinite mathematical objects. This isn't something you could do in real life because a real "sphere" is constructed of a finite number of discrete particles.

>> No.7441866
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7441866

>>7441817

>> No.7441903

>>7441779
It's not that hard to explain intuitively:

There are infinite points on a sphere and if you divide them up in a certain way you get "infinity + infinity". It's really no more surprising than the fact that you can split the whole numbers into evens and odds, then add 1 and divide by 2 to each odd number and divide by 2 to each even number and you now have two copies of the sets you started with without adding any members to the sets.

>> No.7441907

>>7441841
it's been a pop math meme for a while now.
Just check the catalog.
It's just gonna have a resurgence now that there's a popmath video on it.

>> No.7442009

>>7441779
Looking at a topological space as a set of points admits way too many pathological examples. Just work with simplicial sets and things will be fine.

>> No.7442262

>>7441805
Your interpretation is wrong.

>> No.7442305

>>7441820
That's half right. The key point missing is that there are translations and rotations that are necessary to create the decomposition, and these only exist in certain contexts for certain sets. It still has a lot to do with infinite cardinality.

>> No.7442323

>>7442009
>Looking at a topological space as a set of points admits way too many pathological examples. Just work with simplicial sets and things will be fine.
are work in pointless topology

L O C A L E S

>> No.7442418

>>7441903
You are ignorant. Please refrain from giving your opinion as fact on objective matters in mathematics; the machinery behind Banach-Tarski is not analogous to the arithmetic of ordinals.

>> No.7442423

lmao I remember when my calc 2 ta showed this to the class and nobody was interested.

>> No.7442485

>>7441817
where can i learn non-meme tier science without going to collegue?

been lurking for a while now.

>> No.7442495

>>7442323
So much this. It's okay, soon you guys will have the privilege to work with my hodological spaces, which are motivated by the pathologies of analytic topology. Topology should be as synthetic as algebra.

>> No.7442515

>>7442485
textbooks and MOOCs