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...

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

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...

In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself...

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...

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

pattern 231; they are counted by the Catalan numbers, and may be placed in bijection with many other combinatorial objects with the same counting function...

states that continuous bijections of smooth manifolds preserve dimension. That is, there does not exist a continuous bijection between two smooth manifolds...

the Einstein field equations. Specifically, they are a transcendental bijection of the spacetime continuum, an asymptotic projection of the Calabi–Yau...

a group isomorphism is a function between two groups that sets up a bijection between the elements of the groups in a way that respects the given group...

of the vector spaces from which the projective spaces derive. It is a bijection that maps lines to lines, and thus a collineation. In general, some collineations...

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...

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...

{\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...

actions Function composition; transformation group Comparing Enumeration Bijection; cardinal number; order Timing Before & After Linear order Counting Successor...

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...

In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning, such...

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...

same order type if they are order isomorphic, that is, if there exists a bijection (each element pairs with exactly one in the other set) f : X → Y {\displaystyle...

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

union is the coproduct of the category of sets, and thus defined up to a bijection. In this context, the notation ∐ i ∈ I A i {\textstyle \coprod _{i\in...

simply a strictly increasing bijection. This result implies, for example, that there exists a strictly increasing bijection between the set of all rational...

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...

the integers and the even integers into a one-to-one correspondence (or bijection), which is a function that maps between two sets such that each element...

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...