Functional statements

• function is a set

• function is a set the elements of which are ordered pairs

• function is a relation

• function is a binary relation that is functional and serial

• function is a binary relation that is right-unique and left-total

• function (relation) between two sets is an element of their dot product

• identity function is a mapping from a set back to itself

• identity function is identical to the reflexive closure

misc/unsorted

• a relation that is functional means exactly that the relation is a function

• A relation that is injective and functional is precisely an injective function on its domain. It is a bijection of its domain with its range.

• relation need not be total; functions must be total (for now)

• R is a function X -> Y if for each x ∈ X, there is exactly one y ∈ Y such that xRy

• R is a bijection between X and Y if R and its inverse are both functions

Synonyms and near terms

Function, ~AKA

• map

• mapping

• transformation

• correspondence

  • one-to-one correspondence

• adjection

  • surjection, onto

  • injection, one-to-one

  • bijection, one-to-one correspondence, inverse is a function

• association

• functional relation

• morphism (homomorphism, isomorphism)

• arrow

• routine, subroutine

• procedure, subprocedure