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.
--
Steve
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