query: Let $S$ be any infinite set. Is it true that $S \times \mathbb{Z}$ has the same cardinality as $S$?
positive_passages.docid: 23442
positive_passages.text: Cardinality of the union of infinite and countable sets
negative_passages.docid: 85099
negative_passages.text: How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
negative_passages.docid: 127233
negative_passages.text: Cardinality of order types in $\mathbb{N}$
negative_passages.docid: 139078
negative_passages.text: Infinite partition of $\mathbb N$ by infinite subsets
negative_passages.docid: 132537
negative_passages.text: Class of sets of a given infinite cardinality
negative_passages.docid: 122814
negative_passages.text: Finite Sets, Equal Cardinality, Injective $\iff$ Surjective.
negative_passages.docid: 122947
negative_passages.text: What is the cardinality of the set of infinite cardinalities?
negative_passages.docid: 157513
negative_passages.text: How can I prove that these sets are countable infinite?
negative_passages.docid: 13924
negative_passages.text: For all infinite cardinals $\kappa, \ (\kappa \times \kappa, <_{cw}) \cong (\kappa, \in).$
negative_passages.docid: 91237
negative_passages.text: Every infinite set contains a countable subset
negative_passages.docid: 6161
negative_passages.text: The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
negative_passages.docid: 272
negative_passages.text: Cantor Sets/nonempty/cardinality
negative_passages.docid: 86926
negative_passages.text: Why isn't this a well ordering of $\{A\subseteq\mathbb N\mid A\text{ is infinite}\}$?
negative_passages.docid: 117561
negative_passages.text: A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
negative_passages.docid: 106325
negative_passages.text: Question about Cardinality
negative_passages.docid: 45216
negative_passages.text: Cardinality of $[0,1]$
negative_passages.docid: 77548
negative_passages.text: Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?