Re:Functions are Vectors
by slavik81 on Saturday July 29, 2023 @08:31PM
(#36926388)
You may be confused because a bijective function must be one-to-one, while in general, a function may be many-to-one. However, the standard definition of a function excludes one-to-many mappings.
> A function f from a set X to a set Y, denoted f: X -> Y, is a relation from X, the domain, to Y, the co-domain, that satisfies two properties: (1) every element in X is related to some element in Y, and (2) no element in X is related to more than one element in Y.
Susanna S. Epp. 2010. Discrete Mathematics with Applications (4th. ed.). p.384
> A function f from a set X to a set Y, denoted f: X -> Y, is a relation from X, the domain, to Y, the co-domain, that satisfies two properties: (1) every element in X is related to some element in Y, and (2) no element in X is related to more than one element in Y.
Susanna S. Epp. 2010. Discrete Mathematics with Applications (4th. ed.). p.384