surjektio
Surjektio, in mathematics often called a surjection or onto function, is a type of function between sets that covers its codomain. If f is a function from a domain A to a codomain B, f is surjective when every element of B is the image of at least one element of A.
Formally, f: A -> B is surjective if for every b in B there exists an a in
- The function f: Z -> Z given by f(n) = n is surjective (and in fact bijective).
- The function f: R -> R given by f(x) = x^3 is surjective; every real number has a
- The function f: Z -> Z given by f(n) = n^2 is not surjective onto Z (negative integers
- The function f: R -> {0,1} defined by f(x) = 0 if x < 0 and f(x) = 1 if
- The surjectivity of a composition: if f: A -> B and g: B -> C are surjective, then
- In finite sets, a surjective f: A -> B implies |A| ≥ |B|; if f is also injective,
Surjectivity is a fundamental notion in algebra and analysis, often used to describe when every target