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In mathematics, a surjective function (also known as surjection, or onto function / ˈ ɒ n. t uː /) is a function f such that, for every element y of the function's codomain, there exists at least one element x in the function's domain such that f(x) = y. In other words, for a function f : X → Y, the codomain Y is the image of the function ...
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]
Also called an injection or, sometimes, 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 preimage for every element of the codomain, that is, the codomain equals the image. Also called a surjection or onto function.
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
The one-argument function Frege generalizes into the form Φ(A) where A is the argument and Φ( ) represents the function, whereas the two-argument function he symbolizes as Ψ(A, B) with A and B the arguments and Ψ( , ) the function and cautions that "in general Ψ(A, B) differs from Ψ(B, A)".
For every set X, there is a unique function, called the empty function, or empty map, from the empty set to X. The graph of an empty function is the empty set. [note 5] The existence of empty functions is needed both for the coherency of the theory and for avoiding exceptions concerning the empty set in many statements.
(Un) Gazier originally, a man who worked in gas transport; nowadays, it is a familiar way to say "Someone" (mostly for a man; this term is rare for women, and in such case, the correct word is the feminine form "Gazière"). [22] (Un) Quidam: someone whose identity is unknown or cannot be disclosed. [23] See also fr:wikt:Tartempion#Synonymes
For example, if someone needs a paperweight, but they only have a hammer, they may not see how the hammer can be used as a paperweight. Functional fixedness is this inability to see a hammer's use as anything other than for pounding nails; the person couldn't think to use the hammer in a way other than in its conventional function.