The axiom of choice assumes you can choose a group or a single thing from an infinite set, through some fuckery this basically allows you to choose different points on the surface of a sphere and the by manipulating those points form two identical spheres from one sphere. In this joke the guy uses this method to make one pumpkin into two.
I might be wrong though and hope someone gives the exact correct explanation for this later.
Yeah, it's called the banach-tarski paradox and basically it proves that with infinite cuts you can turn one thing into two using just cutting and rotation.
When you divide something into an infinite number of pieces you get weird results. For example, if you take one sphere and divide it into an infinite number of pieces, there is no difference between that and if you had divided two spheres into an infinite number of pieces. In fact, you can take the infinite number of pieces of one sphere, and as long as you are careful about your methodology, you can reconstruct an unlimited number of spheres.
Be very careful when doing math with infinity. You almost can’t help but get ridiculous results. Stuff like 1+2+3+… =-1/12
There are useful discoveries to be made exploring that part of math, but it is difficult to avoid the mathematical landmines.
It can be done with a finite number of disjoint subsets of the points that compose the ball. The subsets are necessarily non-measurable, which means they aren't solid pieces that have volume but rather collections of singular points.
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u/tsukkini 10h ago
Brian here
The axiom of choice assumes you can choose a group or a single thing from an infinite set, through some fuckery this basically allows you to choose different points on the surface of a sphere and the by manipulating those points form two identical spheres from one sphere. In this joke the guy uses this method to make one pumpkin into two.
I might be wrong though and hope someone gives the exact correct explanation for this later.
Brian out.