My understanding is that the infinity of "all integers greater than zero" and of "all integers greater than zero and divisible by 2" are in fact infinities of the _same_ size.

The same would apply for "divisible by 100" or "divisible by 1 million". This would apply to the fraction of worlds that are populated, whatever fraction of them are.

As best I understand it, all those reduce to aleph-zero because they're countably infinite and can be mapped to the natural numbers. But aleph-one exists and is provably bigger than aleph-zero despite both being infinite.

https://en.wikipedia.org/wiki/Aleph_number http://www.alephzero.co.uk/what.htm

Of course. Of course. You are totally right.

https://www.youtube.com/watch?v=23I5GS4JiDg