The identity function iS: S →S, on a set S, is defined by iS(s) = s for all s in S. Identity functions have the property that if f: S → T is a function, then f∘iS = f and iT∘f = f.
Computer
A function
with the property thatSuch a function leaves every element in its domain unaltered. Identity functions are needed for such purposes as the definition of inverses of functions.