Quote:
Originally Posted by whswhs
As for "fake," in both mathematics and RPGs, we start out by making assumptions, which we agree to pretend are true. Within the context of the game, calling them "fake" is not a valid move; to do so is to refuse to play the game. In this case, the game is exploring the concept of a die in the shape of a regular polyhedron with infinitely many sides.
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There's a reason mathematicians treat these sorts of things as limits these days rather than infinities or infinitesimals. I suspect but can't prove that if you build a proper model of constructing an polyhedron of n faces and let n go to infinity that something explodes mathematically in a way it doesn't for continuous infinite variation for a sphere.
I more than half suspect it's going to get you back to the axiom of choice - you know the one that allows you to cut a sphere into two identical spheres.... The math joke is "the Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" - the joke being that's pretty much true by inspection on the superficial definitions, and you can prove all three are restatements of each other.