Cardinality

Statement: The real numbers in [0, 1) can be mapped onto the set of all possible universes.

True / false?

sure, why not.

Not sure what you mean by "universe" but no set can be mapped to it's own power set.

>>3
The proof of this doesn't actually require cardinality, though one of its corollaries is a statement about cardinality.

>>3
Physical universes, as in configurations of matter, space-time topology and any other things in our universe that may be regarded as variable.

True/False:

The continuum is equal to aleph-one

True/False:
The continuum is equal to a guy named Frank who makes balloon animals.

WTF kind of proposition IS this?

FALSE!! Cause even balloon animals die!! Lol

>>1
Do you mean indexing universes?  If the universe is fundamentally discrete in both time and space, then true.  I suppose if you wanted to be fancy you could design some mind-bogglingly huge code to specify all particles and trajectories and then embed it in the decimal expansion, which probably amounts to the same thing.

Of course, at that point, you may as well say that the natural numbers can be mapped to the same set, and go home.

If it isn't discrete, then it's probably undecidable in ZFC.  It sounds equivalent to the continuum hypothesis although fuck me if I know how I'd actually frame the problem rigorously.