Injection vs Surjection - What's the difference?
injection | surjection |
The act of injecting, or something that is injected.
(specifically, medicine) Something injected subcutaneously, intravenously, or intramuscularly by use of a syringe and a needle.
(set theory) A function that maps distinct x in the domain to distinct y in the codomain; formally, a f'': ''X'' → ''Y such that f(a) = f(b) implies a = b for any a, b in the domain.
(mathematics) A relation on sets (X,Y)'' that associates each element of ''Y'' with at most one element of ''X .
(figuratively) The addition of money to someone, or to a business.
(programming) The insertion of program code into an application, URL, hardware, etc.; especially when malicious or when the target is not designed for such insertion.
A specimen prepared by injection.
(steam engines) The act of throwing cold water into a condenser to produce a vacuum.
(steam engines) The cold water thrown into a condenser to produce a vacuum.
(category theory) A morphism from either one of the two components of a coproduct to that coproduct.
(Contruction) The act of inserting materials like concrete grout or gravel by using high pressure pumps.
(set theory) A function of "many-to-one" mapping relationship; more formally, f'': ''X'' → ''Y'' is a surjection if and only if, for every ''y'' in the codomain ''Y'', there is at least one ''x'' in the domain ''X'' with ''f''(''x'') = ''y .
Surjection is a related term of injection.
In set theory terms the difference between injection and surjection
is that injection is a function that maps distinct x in the domain to distinct y in the codomain; formally, a f: X → Y such that f(a) = f(b) implies a = b for any a, b in the domain while surjection is a function of "many-to-one" mapping relationship; more formally, f: X → Y is a surjection if and only if, for every y in the codomain Y, there is at least one x in the domain X with f(x) = y.As nouns the difference between injection and surjection
is that injection is the act of injecting, or something that is injected while surjection is a function of "many-to-one" mapping relationship; more formally, f: X → Y is a surjection if and only if, for every y in the codomain Y, there is at least one x in the domain X with f(x) = y.injection
English
(wikipedia injection)Noun
(en noun)- The troubled business received a much-needed cash injection .
- a SQL injection exploit allowing a malicious user to modify a database query