What does surjective function mean?

Here's a list of possible definitions for the term surjective function:


  1. Surjective function

    In mathematics, a surjective function (also known as surjection, or onto function) is a function f such that every element y can be mapped from element x so that f(x) = y. In other words, every element of the function's codomain is the image of at least one element of its domain. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y. The term surjective and the related terms injective and bijective were introduced by Nicolas Bourbaki, a group of mainly French 20th-century mathematicians who, under this pseudonym, wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. The French word sur means over or above, and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain. Any function induces a surjection by restricting its codomain to the image of its domain. Every surjective function has a right inverse assuming the axiom of choice, and every function with a right inverse is necessarily a surjection. The composition of surjective functions is always surjective. Any function can be decomposed into a surjection and an injection.


  1. Chaldean Numerology

    The numerical value of surjective function in Chaldean Numerology is: 3

  2. Pythagorean Numerology

    The numerical value of surjective function in Pythagorean Numerology is: 9

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