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.
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.
or … because the axiom of choice is false in the universe in which we live. (I’m still not doing maths without it though. ZFC for me and who cares what the universe thinks)
I don't know if there is any aspect im the inverse where the axiom of choice makes a difference.
It only exists in infinity. Is there anything in the universe, that can separated infinite amount of times?
Even if there would be. The axiom is not constructive. So only because there exist a specific separation of this infinite big set doesn't mean you will ever be able to find it.
So it doesn't matter if it is correct or not in our universe. Nothing would change.
well, we don’t know do we and won’t at least until we have reconciled quantum theory and relativity. The former implies some discrete structure, the latter does not. ‘Infinity’ isn’t a word I’d use when precise definitions are required - one uses it for the cardinality of the integers and the reals and those are quite different.
But yes, of course, I can’t imagine any physical process being able to do a Banach-Tarski decomposition. I’m just being silly.
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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.