A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the second set (the...

In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from...

uncountable. Also, by using a method of construction devised by Cantor, a bijection will be constructed between T and R. Therefore, T and R have the same...

(surjection, not a bijection) An injective surjective function (bijection) An injective non-surjective function (injection, not a bijection) A non-injective...

In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f : V ( G ) → V ( H ) {\displaystyle f\colon V(G)\to...

is that no bijection can exist between {1, 2, ..., n} and {1, 2, ..., m} unless n = m; this fact (together with the fact that two bijections can be composed...

(injection, not a bijection) An injective surjective function (bijection) A non-injective surjective function (surjection, not a bijection) A non-injective...

two approaches to cardinality: one which compares sets directly using bijections and injections, and another which uses cardinal numbers. The cardinality...

set is Dedekind-finite if it is not Dedekind-infinite (i.e., no such bijection exists). Proposed by Dedekind in 1888, Dedekind-infiniteness was the first...

and B are equinumerous if there exists a one-to-one correspondence (or bijection) between them, that is, if there exists a function from A to B such that...