The identity relation for a set
The identity relation is a specific type of equivalence relation that fulfills all the standard properties. Which is, for all
- Reflexive:
- Symmetric: If
, then - Transitive: If
and , then
Identity Function
Since the identity relation always have at most one object in the co domain mapped from one object in the domain, it is also a function. We call it identity function, identity map, or identity transformation. The identity function on
The identity function is bijective.
See Also
- the identity predicate - Identity relation in the first-order logic
- identity matrix - Represents an identity linear transformation