Oops, I messed up. (Thanks David for pointing that out.)
On Sun, Oct 18, 2020 at 07:45:40PM +1100, Steven D'Aprano wrote:
Each of these number systems have related, but slightly different, rules. For example, IEEE-754 has a single signed infinity and 2**INF is exactly equal to INF. But in transfinite arithmetic, 2**INF is strictly greater than INF (for every infinity):
2**aleph_0 < aleph_1 2**aleph_1 < aleph_2 2**aleph_2 < aleph_3
I conflated what I was thinking:
# note the change in comparison 2**aleph_0 > aleph_0 2**aleph_1 > aleph_1 2**aleph_2 > aleph_2 ...
which I think is correct regardless of your position on the Continuum Hypothesis (David, care to comment?), with this:
2**aleph_0 = aleph_1 2**aleph_1 = aleph_2 2**aleph_2 = aleph_3 ...
which is only true if the Continuum Hypothesis is true, and then wrote down something which was complete nonsense. Sorry.