> > > A unit lenght 1 times aleph_0 is what? > > > > Nonsense! > > A unit times aleph_0 is aleph_0.
That presumes that Aleph_0 is amenable to some sort of multiplication and division.
A claim that requires proof, as Aleph_0 is not a member of any of the sets of numbers for which multiplication is defined, and is not a unit of measure, like yards or metres, that can be halved or doubled meaningfully. --