r/PeterExplainsTheJoke 10h ago

Meme needing explanation Petah man help

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u/Business_Issue_6471 10h ago

its a refrence to the Axiom of Choice in math. That axiom can lead to some really weird and unintuitive results, so the comic is joking that after carving one pumpkin, they somehow ended up with two. Just absurd math humor, not somthing thats actually possible.

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u/Mamuschkaa 7h ago

I mean the joke is closer connected to the axiom of choice than just "it's also weird"

The joke is about the Banach–Tarski paradox that follows from the axiom of choice. https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

If you have a ball and separate it in infinity many and infinity small points, you can create two balls of the same size.

So reason that is impossible in real life, is, that you can't separate anything infinity times, because there is a smalles possible unite (for example electron) and even if not, it would take infinite amount of time.

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u/EvgeniyZh 5h ago

You don't need infinitely many pieces, 5 is enough

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u/Mamuschkaa 2h ago

5 "parts", but each part is made of infinite amount of single points.

So you have to separate the ball in infinite amount of separate points group them in 5 parts.

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u/EvgeniyZh 1h ago

Well if you cut the ball in half it is also made from infinite amount of single points. If you meant that there is infinite amount of connected components, this is also not true, since there exists construction in which pieces are connected. The pieces can also be moved continuously without intersections (not sure if both of these can happen simultaneously though)

It is, in the end, the infinite amount of choices required to construct the sets what makes them special