Gaming philosophy conundra

[Anthony]

Originally Posted by whswhs

It seems as if it still must be the case that if you represent every number on the apeirohedron as a decimal (which is how Lovewyrm chose to represent them), there must be many numbers whose representation has infinitely many digits and therefore counts as a "sword" of infinite length.

You are guaranteed arbitrary length but not infinite length. I'm actually curious what the difference between a polyhedron with aleph-0 sides and a sphere (same cardinality as the reals; if the continuum hypothesis is true this would be aleph-1) would be.