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
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