Algebraic Property
If f : M → N is any function, then we have f idM = f = idN f (where "" denotes function composition). In particular, idM is the identity element of the monoid of all functions from M to M.
Since the identity element of a monoid is unique, one can alternately define the identity function on M to be this identity element. Such a definition generalizes to the concept of an identity morphism in category theory, where the endomorphisms of M need not be functions.
Read more about this topic: Identity Function
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