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Bijection
In mathematics, a bijection, bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where
Bijection, injection and surjection
In mathematics, injections, surjections and bijections are classes of functions distinguished by the manner in which arguments (input expressions from
Injective function
(injection, not a bijection) An injective surjective function (bijection) A non-injective surjective function (surjection, not a bijection) A non-injective
Surjective function
be surjective. Another surjective function. (This one happens to be a bijection) A non-surjective function. (This one happens to be an injection) A function
Counting
bijection) of the set with the set of numbers {1, 2, ..., n}. A fundamental fact, which can be proved by mathematical induction, is that no bijection
Graph isomorphism
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
Cantor's diagonal argument
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
Countable set
definition of size. To elaborate this we need the concept of a bijection. Although a "bijection" seems a more advanced concept than a number, the usual development
Combinatorial proof
Two sets are shown to have the same number of members by exhibiting a bijection, i.e. a one-to-one correspondence, between them. The term "combinatorial
Real line
The bijection between points on the real line and vectors