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...

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 =...

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

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

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

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...

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...

{\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 ...

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...

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

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...

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...

13 function is an example of a simple-to-define function which takes on every real value in every interval, that is, it is an everywhere surjective function...

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

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...

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...

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

In category theory, a point-surjective morphism is a morphism f : X → Y {\displaystyle f:X\rightarrow Y} that "behaves" like surjections on the category...

{\displaystyle K/k} . A discrete valuation of K / k {\displaystyle K/k} is a surjective function v : K → Z ∪ { ∞ } {\displaystyle v:K\to \mathbb {Z} \cup \{\infty...

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

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...

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...

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

{\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...

characteristic function of a subset A of some set X maps elements of X to the codomain { 0 , 1 } . {\displaystyle \{0,\,1\}.} This mapping is surjective only when...

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...

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...

\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...

rank function. Thus the constant rank theorem applies to a generic point of the domain. When the derivative of F is injective (resp. surjective) at a...