Identity function
An identity function f is a function which doesn't have any effect: it always returns the same value that was used as its argument.
Formally, if M is a set, we define the identity function idM on M to be that function with domain and codomain M which satisfies
- idM(x) = x for all elements x in M.
If f : M → N is any function, then we have f o idM = f = idN o f. In particular, idM is the identity element of the monoid of all functions from M to M.
When choosing M equal to the positive integers, one obtains the identity function Id(n), which is a multiplicative function considered in number theory.
Referenced By
Elementary function | Elementary functions | Laws of Logic | List of basic discrete mathematics topics | List of functions | List of mathematical functions | List of mathematical topics (G-I) | List of mathematical topics (G-Z) | Schrodinger's equation | Schrodinger equation | Schrodinger wave equation | Schrodingers equation | Schroedinger's equation | Schroedinger equation | Schrödinger Wave Equation | Schrödinger equation | Special function | Special functions
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