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...

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...

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

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

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...

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...

isomorphism if it satisfies the following properties f {\displaystyle f} is a bijection f {\displaystyle f} is uniformly continuous the inverse function f − 1...

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

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...

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...

other sets that are easier to count. Additionally, the nature of the bijection itself often provides powerful insights into each or both of the sets...

same cardinality if, and only if, there is a one-to-one correspondence (bijection) between the elements of the two sets. In the case of finite sets, this...

{\displaystyle F\subseteq Y} such that the restriction of f to E is a bijection from E to F, and has thus an inverse. The inverse trigonometric functions...

consecutive integers, that is, those S for which {i, i + 1} ⊈ S for every i. A bijection with the sums to n+1 is to replace 1 with 0 and 2 with 10, and drop the...

mathematical analysis, an isomorphism between two Hilbert spaces is a bijection preserving addition, scalar multiplication, and inner product. In early...

{\displaystyle f} is a bijection between its elements in A and its elements in B. For a B-stopper, the function g {\displaystyle g} is a bijection between its elements...

a given set S of n elements in some fixed order, which establishes a bijection from an interval of ( n k ) {\displaystyle {\tbinom {n}{k}}} integers...

Cartesian coordinates is given by x = r cosθ and y = r sinθ. With every bijection from the space to itself two coordinate transformations can be associated:...

According to the second meaning, a permutation of a set S is defined as a bijection from S to itself. That is, it is a function from S to S for which every...

of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a linear isomorphism. In the case where V = W {\displaystyle...

This bijection then expands to the bijection X = A + B + A + B + ⋯ + Z. Substituting the right hand side for X in Y = B + X gives the bijection Y = B...

Bijection between 3-subsets of a 7-set (left) and 3-multisets with elements from a 5-set (right) So this illustrates that ( 7 3 ) = ( ( 5 3 ) ) . {\textstyle...

Further, by the definition of a functor, if φ is a bijection between sets A and B, then F[φ] is a bijection between the sets of F-structures F[A] and F[B]...

and B {\displaystyle B} there exists a feasible exchange bijection, defined as a bijection f {\displaystyle f} from A {\displaystyle A} to B {\displaystyle...

uniformly continuous bijection with a uniformly continuous inverse). They are called bilipschitz homeomorphic if there is a bilipschitz bijection between them...

sequence is S. The immediate consequence is that Prüfer sequences provide a bijection between the set of labeled trees on n vertices and the set of sequences...

Bijection between 3 bit binary numbers and compositions of 4...

path p : [ 0 , 1 ] → X {\displaystyle p:[0,1]\to X} in X determines a bijection F p ( 0 ) → ∼ F p ( 1 ) . {\displaystyle {\mathcal {F}}_{p(0)}{\overset...