08-08-2021, 12:27 AM

Hilbert's infinite hotel seems to contain infinities within infinities. But those are what I call (using Aristotle's term) potential infinities, not 'completed' infinities as in Cantor's transfinite numbers. In my view it's impossible to have a completely full Hilbert's infinite hotel since there isn't any largest room number. It's impossible to fill the entire hotel with guests in the first place!