andrewducker: (Default)
andrewducker ([personal profile] andrewducker) wrote2012-07-17 12:00 pm

[identity profile] steer.livejournal.com 2012-07-19 10:03 am (UTC)(link)
Surely Mr Spacelem you must at least address the continuum hypothesis if you're counting the infinities.

I would answer "there are *at least* two infinities" -- the ones you state (aleph nought and c). We do not know if aleph one is the same as c -- and it may require extra axioms in our chosen set theory.

http://en.wikipedia.org/wiki/Continuum_hypothesis

Incidentally, Rudy Rucker's terrific but weird "White Light or What Is Cantor's Continuum Problem?" addresses the issue in a scifi way with lots of drugs and giant talking cockroaches.
Edited 2012-07-19 10:04 (UTC)