mathematics, a 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...

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

domain; that is, if the image and the codomain of the function are equal. A surjective function is a surjection. Notationally: ∀ y ∈ Y , ∃ x ∈ X , y =...

codomain and the image of a function are the same set; such a function is called surjective or onto. For any non-surjective function f : X → Y , {\displaystyle...

set X is equivalent to counting injective functions N → X when n = x, and also to counting surjective functions N → X when n = x. Counting multisets of...

element of Y. Functions which satisfy property (3) are said to be "onto Y " and are called surjections (or surjective functions). Functions which satisfy...

{\displaystyle y\in Y} implies that f is surjective. The inverse function f −1 to f can be explicitly described as the function f − 1 ( y ) = ( the unique element ...

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...

element x in the domain X. The identity function on X is clearly an injective function as well as a surjective function (its codomain is also its range), so...

thus f − 1 ( y ) = { x } . {\displaystyle f^{-1}(y)=\{x\}.} The function f is surjective (or onto, or is a surjection) if its range f ( X ) {\displaystyle...

composition of one-to-one (injective) functions is always one-to-one. Similarly, the composition of onto (surjective) functions is always onto. It follows that...

analogues of onto or surjective functions (and in the category of sets the concept corresponds exactly to the surjective functions), but they may not exactly...

ideal is called a place of K/k. A discrete valuation of K/k is a surjective function v : K → Z∪{∞} such that v(x) = ∞ iff x = 0, v(xy) = v(x) + v(y) and...

injective function from S {\displaystyle S} to N {\displaystyle \mathbb {N} } . S {\displaystyle S} is empty or there exists a surjective function from N...

Riemann-integrable. The Peano space-filling curve is a continuous surjective function that maps the unit interval [ 0 , 1 ] {\displaystyle [0,1]} onto...

elements of a set J, then J is an index set. The indexing consists of a surjective function from J onto A, and the indexed collection is typically called an...

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept...

well-order. Since the collection of all ordinals such that there exists a surjective function from B {\displaystyle B} to the ordinal is a set, there exists an...

simple-to-understand function which takes on every real value in every interval, that is, it is an everywhere surjective function. It is thus discontinuous...

one-to-one function. In other words, every element of the function's codomain is the image of at most one element of its domain. Surjective function: has a...

\Omega } is a univalent function such that f ( G ) = Ω {\displaystyle f(G)=\Omega } (that is, f {\displaystyle f} is surjective), then the derivative of...

In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is...

In mathematics, the restriction of a function f {\displaystyle f} is a new function, denoted f | A {\displaystyle f\vert _{A}} or f ↾ A , {\displaystyle...

this equivalence. Any injective function between two finite sets of the same cardinality is also a surjective function (a surjection). Similarly, any surjection...

example, to say that a function is onto (surjective) or not the codomain should be taken into account. The graph of a function on its own does not determine...

cardinality of S is less than the cardinality of T, then there is no surjective function from S to T. Let q1, q2, ..., qn be positive integers. If q 1 + q...

{\displaystyle \left(a_{1},\ldots ,a_{n}\right)} may be identified with the (surjective) function F   :   { 1 , … , n }   →   { a 1 , … , a n } {\displaystyle F~:~\left\{1...

on a quotient space is a final topology, with respect to a single surjective function, namely the quotient map. The disjoint union topology is the final...

objects. For example, every function may be factored into the composition of a surjective function with an injective function. Matrices possess many kinds...

mathematical analysis and its applications, a function of several real variables or real multivariate function is a function with more than one argument, with all...