Who was Aleph Null? (2013)

Re:Who was Aleph Null? (2013) by guerrilla on Thursday October 14, 2021 @01:15PM (#28867093)

I am also rusty, but I believe both statements are true but mine may be more precise as there is more than one uncountable infinite set and the set of all countable ordinal numbers is an uncountable infinite set.

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Re:Who was Aleph Null? (2013) by brobdingnagians on Thursday October 14, 2021 @01:21PM (#28867177)

The cardinality of Real numbers is 2^Aleph_Null. Continuum hypothesis is equivalent to saying that it is equal to Aleph_One. But that is debated :) [Debated in the sense that you could accept one or the other, but it is independent of ZF and there should be a good reason to accept one or the other]

https://en.wikipedia.org/wiki/Aleph_number#Aleph-one

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Re:Who was Aleph Null? (2013) by guerrilla on Thursday October 14, 2021 @01:30PM (#28867293)

> but it is independent of ZF

Yeah, if I recall that's why forcing was invented, to specifically prove that C and CH were independent of ZF. Yeah: [1]

1. https://en.wikipedia.org/wiki/Paul_Cohen#Continuum_hypothesi...

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Re:Who was Aleph Null? (2013) by bialpio on Thursday October 14, 2021 @02:25PM (#28868007)

You're right, I got thrown off by the "countable" part in the "set of countable ordinal numbers", which is indeed uncountably infinite.

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