Count whole #s like 1, 2, 3, 4, 5, 6, 7... forever.
That's Aleph(0) long, but countable. You can't finish, but you don't need to skip any.
Count decimal #s forever (in order). No matter how you list them, there's some in-between the ones you counted:
If I count "1.0, 1.1, " the I skipped 1.05. If I count that, I've missed 1.02. Etc.
That's Aleph(1) long, and "uncountable".
With Aleph(0), it'd take infinite(Aleph(0)) time to reach the end.
With Aleph(0), it'd take aleph(0) time to get from 1 to 2, and reaching the end takes even longer than infinite.
We call that longer than infinite amount Aleph(1).
It's been proven (don't ask how), that
Aleph(0) ^ Aleph(0) = Aleph(1)
There's also aleph 2, and, 3, and every other number, but I don't understand those. Ask a mathematician.