query: $\Bbb N$x$\Bbb N$ is countably infinite
positive_passages.docid: 27937
positive_passages.text: Cartesian Product of Two Countable Sets is Countable
negative_passages.docid: 102113
negative_passages.text: Proof that the number of proofs is countably infinite
negative_passages.docid: 99478
negative_passages.text: countably infinite union of countably infinite sets is countable
negative_passages.docid: 19297
negative_passages.text: Is the cofinite topology on an uncountable set first countable?
negative_passages.docid: 105358
negative_passages.text: In a second countable space any base has a countable subset that is still a base
negative_passages.docid: 52429
negative_passages.text: Explicit countable elementary extension of $\mathbb{N}$
negative_passages.docid: 151295
negative_passages.text: Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
negative_passages.docid: 69838
negative_passages.text: Does a countably infinite power set exist?
negative_passages.docid: 9651
negative_passages.text: Cardinality of cartesian product of an infinite set with N
negative_passages.docid: 111008
negative_passages.text: Show that $X $ is a infinite set ,it is connected in the finite complement topology?
negative_passages.docid: 154578
negative_passages.text: Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
negative_passages.docid: 67050
negative_passages.text: Every separable metric space has a countable base
negative_passages.docid: 76240
negative_passages.text: How is $\epsilon_0$ countable?
negative_passages.docid: 66301
negative_passages.text: The cardinality of the set of countably infinite subsets of an infinite set
negative_passages.docid: 41661
negative_passages.text: Show that the set of all finite subsets of $\mathbb{N}$ is countable.
negative_passages.docid: 23442
negative_passages.text: Cardinality of the union of infinite and countable sets
negative_passages.docid: 67295
negative_passages.text: Please check my proof for $N$ is infinite