The set of all subsets of $\nats$

Example · Undergraduate

Terms

Term	This example	Why
infinite	✓
uncountable	✓	By Cantor’s theorem, no set is in bijection with the set of all of its subsets.
finite	✗	The set of all subsets of $\nats$ is not finite, because it is uncountable.
countable	✗	The set of all subsets of $\nats$ is not countable, because it is uncountable.
countably infinite	✗

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