Definition
Formally, if M is a set, the identity function f on M is defined to be that function with domain and codomain M which satisfies
- f(x) = x for all elements x in M.
In other words, the function assigns to each element x of M the element x of M.
The identity function f on M is often denoted by idM.
In terms of set theory, where a function is defined as a particular kind of binary relation, the identity function is given by the identity relation, or diagonal of M.
Read more about this topic: Identity Function
Famous quotes containing the word definition:
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)