In mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the...

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for...

surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's codomain, there...

Identity (equation) Identity function Inverse element Monoid Pseudo-ring Quasigroup Unital (disambiguation) Weisstein, Eric W. "Identity Element". mathworld...

up identity in Wiktionary, the free dictionary. Identity may refer to: Identity document Identity (philosophy) Identity (social science) Identity (mathematics)...

systems, identity management can involve five basic functions: The pure identity function: Creation, management and deletion of identities without regard...

-dimensional vector space to itself, the identity matrix I n {\displaystyle I_{n}} represents the identity function, for whatever basis was used in this representation...

f^{-1}=\operatorname {id} _{Y},} where idX is the identity function on the set X; that is, the function that leaves its argument unchanged. In category...

computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers...

mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the...

particular, the identity function X → X {\displaystyle X\to X} is always injective (and in fact bijective). If the domain of a function is the empty set...

function g : Y → X , {\displaystyle g:Y\to X,} the inverse of f, such that each of the two ways for composing the two functions produces an identity function:...

In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all...

The complex conjugate function z → z* is not complex analytic, although its restriction to the real line is the identity function and therefore real analytic...

{\displaystyle x} ; constant functions are idempotent; the identity function is idempotent; the floor, ceiling and fractional part functions are idempotent; the...

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just...

the square function satisfies the identity x2 = (−x)2. This can also be expressed by saying that the square function is an even function. The squaring...

to the identity function λ x . x {\displaystyle \lambda x.x} . In lambda calculus, functions are taken to be 'first class values', so functions may be...

the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial...

systematic lists of some of the many thousands of published identities involving the hypergeometric function, see the reference works by Erdélyi et al. (1953) and...

the sine function and the identity function is sin ⁡ ( 0 ) = 0 {\displaystyle \sin(0)=0} . The only real fixed point of the cosine function is called...

b {\displaystyle b} are also known as exponential functions, and satisfy the exponentiation identity: b x + y = b x b y  for all  x , y ∈ R . {\displaystyle...

mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value...

form eiτ = 1 is that rotating by a full turn is an identity function. Complex number Euler's identity Integration using Euler's formula History of Lorentz...

preserves the identity function and composition of functions: fmap id = id fmap (g . h) = (fmap g) . (fmap h) (where . stands for function composition)...

suppose that the distribution function is the normal distribution with constant variance and the link function is the identity, which is the canonical link...

In other words, A = B is an identity if A and B define the same functions, and an identity is an equality between functions that are differently defined...

{\displaystyle f\colon \mathbb {N} \to \mathbb {N} } is simply the identity function. Z {\displaystyle \mathbb {Z} } , the set of integers is enumerable...

congruences and identities; these are treated separately in the article Ramanujan's sum. A related function is the divisor summatory function, which, as the...

{\displaystyle \left(f|_{B}\right)|_{A}=f|_{A}.} The restriction of the identity function on a set X {\displaystyle X} to a subset A {\displaystyle A} of X...