query: Proof of Natural set to any power k, is countably infinite
positive_passages.docid: 110635
positive_passages.text: Proving $\mathbb{N}^k$ is countable
negative_passages.docid: 20085
negative_passages.text: What's the cardinality of all sequences with coefficients in an infinite set?
negative_passages.docid: 19924
negative_passages.text: Uncountable ordinals without power set axiom
negative_passages.docid: 71922
negative_passages.text: Prove Uncountable set minus a countable set is uncountable
negative_passages.docid: 148516
negative_passages.text: Proof that $\omega^\omega$ is completely metrizable and second countable
negative_passages.docid: 41661
negative_passages.text: Show that the set of all finite subsets of $\mathbb{N}$ is countable.
negative_passages.docid: 103769
negative_passages.text: The Cartesian product of a finite number of countable sets is countable
negative_passages.docid: 31509
negative_passages.text: Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?
negative_passages.docid: 84936
negative_passages.text: The set of all finite sequences of members of a countable set is also countable
negative_passages.docid: 147920
negative_passages.text: Infinite powering by $i$
negative_passages.docid: 43268
negative_passages.text: How to prove that the set of rational numbers are countable?
negative_passages.docid: 127362
negative_passages.text: How do I prove that there doesn't exist a set whose power set is countable?
negative_passages.docid: 91163
negative_passages.text: Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
negative_passages.docid: 100333
negative_passages.text: Show A is countable infinity
negative_passages.docid: 100726
negative_passages.text: Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
negative_passages.docid: 23608
negative_passages.text: Prove the set of all infinite binary sequences is uncountable by using Cantor's theorem.
negative_passages.docid: 66398
negative_passages.text: Union of a finite set and a countably infinite set is countably infinite