3 ms·
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 count
by guerrilla 5y ago
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.
- brobdingnagians 5y agoThe 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 https://en.wikipedia.org/wiki/Aleph_number#Aleph-one
- guerrilla 5y ago> 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_hypothesis https://en.wikipedia.org/wiki/Paul_Cohen#Continuum_hypothesi...
- bialpio 5y agoYou're right, I got thrown off by the "countable" part in the "set of countable ordinal numbers", which is indeed uncountably infinite.