A bijective function from a set to itself is also called a permutation.

So multiplication by g acts as a bijective function.

Of course any bijective function will do, but for convenience's sake linear function is the best.

Cardinality is defined in terms of bijective functions.

A bijective function is a bijection.

An order-isomorphism is a monotone bijective function that has a monotone inverse.

For finite sets, "permutations" and "bijective functions" refer to the same operation, namely rearrangement.

Sets in such a correlation are often called equipollent, and the correlation itself is called a bijective function.

The following theorem gives equivalent formulations in terms of a bijective function or a surjective function.

Mathematically a bijective function is used on the characters' positions to encrypt and an inverse function to decrypt.

Bijective proofs prove that two sets have the same number of elements by finding a bijective function (one-to-one correspondence) from one set to the other.

The term one-to-one function must not to be confused with one-to-one correspondence which is an alternative term for a bijective function.

In mathematics, a bijection (or bijective function or one-to-one correspondence) is a function giving an exact pairing of the elements of two sets.

Bijective functions are essential to many areas of mathematics including the definitions of isomorphism, homeomorphism, diffeomorphism, permutation group, and projective map.

For alternative (equivalent) formulations of the definition in terms of a bijective function or a surjective function, see the section Formal definition and properties below.

A has cardinality strictly greater than the cardinality of B if there is an injective function, but no bijective function, from B to A.

In mathematics, Borel isomorphism is a Borel measurable bijective function from one Polish space to another Polish space.

Cantor defined cardinality in terms of bijective functions: two sets have the same cardinality if and only if there exists a bijective function between them.

In formal mathematical terms, a bijective function f: X Y is a one to one and onto mapping of a set X to a set Y.

It can be shown by transfinite induction that every well-ordered set is order-isomorphic to exactly one of these ordinals, that is, there is an order preserving bijective function between them.

Let G denote the set of bijective functions over A that preserve the partition structure of A: x A g G (g(x) [x]).

The symmetric group on a finite set X is the group whose elements are all bijective functions from X to X and whose group operation is that of function composition.

Formally, given two posets and , an order isomorphism from to is a bijective function from to with the property that, for every and in , if and only if .

If X and Y are spaces, a homeomorphism from X to Y is a bijective function f : X Y such that f and f are continuous.

A permutation of a set X, which is a bijective function , is called a cycle if the action on X of the subgroup generated by has exactly one orbit with more than a single element.