SURJECTIVE Meaning and
Definition
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Surjective, also known as onto function or a surjection, is a term used in mathematics to describe the nature of a function between two sets. In particular, a function is said to be surjective if every element in the codomain (target set) has a preimage in the domain (source set). In simpler terms, a surjective function "covers" or "maps onto" its entire range.
To illustrate this, consider a function f: A → B. If every element y ∈ B has at least one corresponding element x ∈ A, such that f(x) = y, then the function f is surjective. This means that for each value in the codomain B, there exists at least one input value in the domain A that produces it when plugged into the function.
The notion of surjectivity is closely related to injectivity and bijectivity. While an injective function maps each input element to a distinct output element, a surjective function ensures that every output element has an associated input element. A bijective function possesses both surjectivity and injectivity, resulting in a one-to-one correspondence between the elements of the domain and codomain.
Surjective functions have various applications in mathematics, computer science, and other fields. They are often used to establish relationships between different sets or to describe mappings that cover the entire range of a given function.
Common Misspellings for SURJECTIVE
- aurjective
- zurjective
- xurjective
- durjective
- eurjective
- wurjective
- syrjective
- shrjective
- sjrjective
- sirjective
- s8rjective
- s7rjective
- suejective
- sudjective
- sufjective
- sutjective
- su5jective
- su4jective
- surhective
- surnective
Etymology of SURJECTIVE
The word "surjective" is derived from the prefix "sur-" and the root "jective".
The prefix "sur-" comes from the Latin prefix "super-", meaning "above" or "over", which indicates a direction toward greater or higher degree. In mathematics, the prefix "sur-" is often used to indicate a more general or complete version of a concept. For example, "surround" means to enclose completely, "surpass" means to exceed or go beyond, and "survive" means to continue living.
The root "jective" is derived from the Latin verb "iacere", meaning "to throw". In mathematics, the term "objective" is commonly used to refer to a function or mapping, representing a "throwing" of the elements of one set onto another set. This idea of "throwing" or mapping elements corresponds to the more general concept of a function or mapping in mathematics.
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