query: $\kappa\cdot\kappa= \kappa,$ for infinite cardinals
positive_passages.docid: 13924
positive_passages.text: For all infinite cardinals $\kappa, \ (\kappa \times \kappa, <_{cw}) \cong (\kappa, \in).$
negative_passages.docid: 75019
negative_passages.text: Infinite Cartesian product of countable sets is uncountable
negative_passages.docid: 127233
negative_passages.text: Cardinality of order types in $\mathbb{N}$
negative_passages.docid: 120562
negative_passages.text: If A is an infinite set and B is at most countable set, prove that A and $A \cup B$ have the same cardinality
negative_passages.docid: 72190
negative_passages.text: Topological proof on discrete topology where $X$ is infinite
negative_passages.docid: 32965
negative_passages.text: Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
negative_passages.docid: 89167
negative_passages.text: Cardinality of equivalence relations in $\mathbb{N}$
negative_passages.docid: 93330
negative_passages.text: Cardinality of all cardinalities
negative_passages.docid: 97697
negative_passages.text: Countable union of sets of cardinality $c$ has cardinality $c$
negative_passages.docid: 12436
negative_passages.text: The cardinality of the set of all finite subsets of an infinite set
negative_passages.docid: 119624
negative_passages.text: A Dedekind infinite set has a countably infinite proper subset
negative_passages.docid: 116146
negative_passages.text: A cardinal $\kappa$ such that $2^{\lambda}<\kappa$ for all $\lambda<\kappa$ is regular?
negative_passages.docid: 136094
negative_passages.text: $G_\delta$ singletons in compact Hausdorff and first countability
negative_passages.docid: 122947
negative_passages.text: What is the cardinality of the set of infinite cardinalities?
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: 58267
negative_passages.text: Godel's pairing function and proving c = c*c for aleph cardinals
negative_passages.docid: 134071
negative_passages.text: If A is a finite set and B is an infinite set, then B\A is an infinite set