# Linked Questions

11 questions linked to/from Do $\omega^\omega=2^{\aleph_0}=\aleph_1$?
2answers
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### Is it true that $|\mathbb{R}|=2^\omega=\omega_1$? [duplicate]

Is it true that $|\mathbb{R}|=2^\omega=\omega_1$? Note that $\omega_1$ is the successor of $\omega$ and $2^\omega$ is |all functions from $\omega$ to 2|.
4answers
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### How is $\epsilon_0$ countable?

In Wikipedia, it says that any epsilon number with the index that is countable is countable. How is it? Out of all those numbers, I especially want to know why $\epsilon_0$ is countable. Thanks.
3answers
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1answer
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### order of infinite countable ordinal numbers

I'm trying to understand ordinal arithmetic. If one had an ordered list of the some subset of countable ordinal numbers, what order would the following 6 countably infinite ordinals be in? If the ...