What is the power set of Aleph-1?

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Set Theory

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After watching one of V-sauce's videos, I went into a rabbithole about infinity and surreal numbers etc...

If my understanding is correct, the powerset of Aleph-0 or 2^Aleph-0 is an Aleph number somewhere between Aleph-1 and Aleph-w. However, I couldn't find any information about the powerset of Aleph-1.

Does it stay the same as Aleph-1 because of some property of uncountable numbers? If not, does it have some higher limit above Aleph-w?

I'm just the average Joe who thought infinity was cool, so sorry if my question is kind of stupid. Thanks!

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Posted: 3 months ago
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