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A function is bijective if it is both injective and surjective. A bijective function is also called a bijection or a one-to-one correspondence (not to be confused with one-to-one function, which refers to injection). A function is bijective if and only if every possible image is mapped to by exactly one argument. [1]
A bijective function from a set to itself is also called a permutation, [1] and the set of all permutations of a set forms its symmetric group. Some bijections with further properties have received specific names, which include automorphisms, isomorphisms, homeomorphisms, diffeomorphisms, permutation groups, and most geometric transformations.
Also called a surjection or onto function. Bijective function: is both an injection and a surjection, and thus invertible. Identity function: maps any given element to itself. Constant function: has a fixed value regardless of its input. Empty function: whose domain equals the empty set. Set function: whose input is a set.
A function may also be called a map or a mapping, ... For example, the natural logarithm is a bijective function from the positive real numbers to the real numbers.
One-to-one function, also called an injective function; One-to-one correspondence, also called a bijective function; One-to-one (communication), the act of an individual communicating with another; One-to-one (data model), a relationship in a data model; One to one computing (education), an initiative for a computer for every student
In mathematics, an injective function (also known as injection, or one-to-one function [1]) is a function f that maps distinct elements of its domain to distinct elements of its codomain; that is, x 1 ≠ x 2 implies f(x 1) ≠ f(x 2) (equivalently by contraposition, f(x 1) = f(x 2) implies x 1 = x 2).
A bijective function, f: X → Y, from set X to set Y demonstrates that the sets have the same cardinality, in this case equal to the cardinal number 4. Aleph-null, the smallest infinite cardinal. In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set.
The set of bijective isometries from a metric space to itself forms a group with respect to function composition, called the isometry group. There is also the weaker notion of path isometry or arcwise isometry: A path isometry or arcwise isometry is a map which preserves the lengths of curves; such a map is not necessarily an isometry in the ...