query: Proof that for infinite sets, bijections and injections are equivalent
positive_passages.docid: 22240
positive_passages.text: Every infinite subset of a countable set is countable.
negative_passages.docid: 67066
negative_passages.text: Proof there is a 1-1 correspondence between an uncountable set and itself minus a countable part of it
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: 62936
negative_passages.text: Proving equivalencies of two versions of the Axiom of Choice
negative_passages.docid: 95086
negative_passages.text: Homeomorphism is bijective
negative_passages.docid: 152613
negative_passages.text: Injection from $\mathbb{N}\to\{0,1\}$ to the set of all monotonic decreasing functions from $\mathbb{N}\to\mathbb{Z}$
negative_passages.docid: 67451
negative_passages.text: Building a bijection from a finite union of countable sets to $\mathbb{N}$
negative_passages.docid: 149673
negative_passages.text: Cardinality of an infinite union of finite sets
negative_passages.docid: 84301
negative_passages.text: Showing that some Function on the Unit Disc is injective
negative_passages.docid: 30021
negative_passages.text: Bijection between set of all binary sequences and power set of $\mathbb N$.
negative_passages.docid: 36281
negative_passages.text: A set is infinite iff it is equivalent to a proper subset of itself
negative_passages.docid: 98518
negative_passages.text: Cardinality of equivalence relations on N
negative_passages.docid: 124333
negative_passages.text: A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?
negative_passages.docid: 128966
negative_passages.text: Explicit bijection between $\Bbb R$ and permutations of $\Bbb N$
negative_passages.docid: 81682
negative_passages.text: Proving the algebraic set corresponding to a polynomial is infinite.
negative_passages.docid: 148731
negative_passages.text: Constructing a bijection between $[a,b)$ to $(0,1)$
negative_passages.docid: 32340
negative_passages.text: Continuous bijections and their inverses