Identity#
An identity function is a special mapping on a set that returns every element exactly as it was given. Written as \(i_A\) or \(id_A:A→A\), it is formally defined by the rule \(id_A(x) = x\) for every \(x \in A\).
Key Characteristics
- Equivalence
Every input value matches its output value with no change.
- Bijectivity
It is always both injective and surjective, forming a perfect one-to-one corresspondence with itself.
- Self-Inverse
The inverse of an identity function is itself (\(id_A^{-1} = id_A\)).
- Composition Neutrality
Composing any function \(f\) with an identity function leaves \(f\) unchanged (\(f \circ \text{id} = \text{id} \circ f = f\)).
Source: GeeksforGeeks#