Can someone explain the banach-tarski-paradoxon to me? I just

>>9122133
Something people who think they're smart say to people who think they're dumb to make the people who think they're smart seem smart while making the people who think they're dumb seem dumb.

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you may only shitpost ITT with banach-tarski digits

>>9122133
>>9122166
>>9122177
damn

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>>9122183
*THUNK*

*tsssss*

>>9122133
>>9122166
>>9122177
good shit lads

It's math with no clean physical analogue. That always makes people uncomfortable. There isn't a way in real life to automatically choose infinitely small slices of a sphere and put them back together, there's hard physical limits like matter being composed of atoms.

>>9122204
I don't know. Our professor said that the contradiction lies in the unification of disjoint sets compared to the unification of the same sets with some movement.

So that would be an physical analogy.

>>9122133
There's no contradiction, it's named a paradox just because it's counterintuitive

>>9122204
>banach-tarski-paradoxon
It actually says a finite number of pieces (in fact, just 5 pieces suffice).

>>9123464
...but each piece is an immesurable set, with infinite density. so when you split infinity in half, you end up with infinity again.

>>9122133
> I just don't get the contradiction
no contradiction, seems legit

>>9122204
>It's math with no clean physical analogue

No, that's the response to it. The paradox is that the volume of an object can be less than the sum of its parts which anyone will tell you is absurd.

>>9122133
It's the same thing as the infinite hotel thing. Infinity causes this shit to occur, but real life is not infinitely subdividable, so you have no need to worry.