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

confused with one-to-one correspondence that refers to bijective functions, which are functions such that each element in the codomain is an image of exactly...

} The function f is bijective (or is a bijection or a one-to-one correspondence) if it is both injective and surjective. That is, f is bijective if, for...

one element of the domain; that is, if the function is both injective and surjective. A bijective function is also called a bijection. That is, combining...

f exists if and only if f is bijective, and if it exists, is denoted by f − 1 . {\displaystyle f^{-1}.} For a function f : X → Y {\displaystyle f\colon...

if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B. In terms of the...

unique; the function f may map one or more elements of X to the same element of Y. The term surjective and the related terms injective and bijective were introduced...

set Y with a binary relation S then an isomorphism from X to Y is a bijective function f : X → Y {\displaystyle f:X\to Y} such that: S ⁡ ( f ( u ) , f (...

the sets in two combinatorial classes have equal size, by finding a bijective function that maps one set one-to-one onto the other. This technique can be...

generated by these functions. The set of all bijective functions f: X → X (called permutations) forms a group with respect to function composition. This...

ways correspond to way w. Bijective proofs prove that two sets have the same number of elements by finding a bijective function (one-to-one correspondence)...

variable with joint density f. If y = G(x), where G is a bijective, differentiable function, then y has density pY: p Y ( y ) = f ( G − 1 ( y ) ) | det...

(mouse) tumors The Gompertz function is a one-to-one correspondence (also known as an Bijective function) and so its inverse function can be explicitly expressed...

partial functions. A partial function is said to be injective, surjective, or bijective when the function given by the restriction of the partial function to...

maps I {\displaystyle I} bijectively onto the open interval J = f ( I ) {\displaystyle J=f(I)} , and such that the inverse function f − 1 : J → I {\displaystyle...

the inverse function f − 1 {\displaystyle f^{-1}} need not be continuous. A bijective continuous function with a continuous inverse function is called a...

calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the...

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

define a true inverse function, one must restrict the domain to an interval where the function is monotonic, and is thus bijective from this interval to...

among the infinite cardinals. Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, there is a one-to-one...

the interval (−π, π]. This leads to the complex logarithm being a bijective function taking values in the strip R + + i ( − π , π ] {\displaystyle \mathbb...

as Hilbert spaces). In other words, a unitary transformation is a bijective function U : H 1 → H 2 {\displaystyle U:H_{1}\to H_{2}} between two inner product...

The Möbius function μ ( n ) {\displaystyle \mu (n)} is a multiplicative function in number theory introduced by the German mathematician August Ferdinand...

historical convenience. Since gross tonnage is a bijective function of ship volume, it has an inverse function, namely ship volume from gross tonnage, but...

perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the entire...

or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are...

identity function on X is clearly an injective function as well as a surjective function (its codomain is also its range), so it is bijective. The identity...

In mathematics, a Borel isomorphism is a measurable bijective function between two standard Borel spaces. By Souslin's theorem in standard Borel spaces...

a surjection or onto function. Bijective function: is both an injection and a surjection, and thus invertible. Identity function: maps any given element...

In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle...