query: Countability as bijective correspondence
positive_passages.docid: 145428
positive_passages.text: Set $A$ is countably infinite if and only if there exists a bijection $f: \mathbb{N} \rightarrow A$
negative_passages.docid: 155168
negative_passages.text: Is the collection of finite subsets of $\mathbb{Z}$ countable?
negative_passages.docid: 153652
negative_passages.text: Countable ordinals are embeddable in the rationals $\Bbb Q$ -- proofs and their use of AC
negative_passages.docid: 45878
negative_passages.text: Elementary Set Theory: Ordinals, Well Orderings and Isomorphisms
negative_passages.docid: 78225
negative_passages.text: Countable additivity implies countable subadditivity?
negative_passages.docid: 52798
negative_passages.text: Finding counterexamples: bijective continuous functions that are not homeomorphisms
negative_passages.docid: 53101
negative_passages.text: Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
negative_passages.docid: 146436
negative_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?
negative_passages.docid: 132868
negative_passages.text: Bijection between an infinite set and its union of a countably infinite set
negative_passages.docid: 153651
negative_passages.text: Countable partition in atoms
negative_passages.docid: 55717
negative_passages.text: cardinality of the Borel $\sigma$-algebra of a second countable space
negative_passages.docid: 45792
negative_passages.text: Rigorous proof that surjectivity implies injectivity for finite sets
negative_passages.docid: 97697
negative_passages.text: Countable union of sets of cardinality $c$ has cardinality $c$
negative_passages.docid: 91938
negative_passages.text: Countable Matrix Representation
negative_passages.docid: 66301
negative_passages.text: The cardinality of the set of countably infinite subsets of an infinite set
negative_passages.docid: 65910
negative_passages.text: Reflexivity of equivalence relations
negative_passages.docid: 157081
negative_passages.text: The cartesian product of a finite amount of countable sets is countable.