Identity Relation

Identity Relation

## Definition / Concept

The identity relation on $A$ relates every element only to itself.

## Formula

$$I_A=\{(a,a):a\in A\}$$

If:

$$n(A)=n$$

then:

$$n(I_A)=n$$

## Conditions / Special Cases

The identity relation is reflexive, symmetric and transitive.

Therefore:

$$I_A\text{ is an equivalence relation}$$

## Usage

- Used as a standard example of an equivalence relation.