The identity relation for a set is a binary relation that consists of ordered pairs in the form . In other words, each element is related only to itself. We usually denote the identity relation using the equality symbol . For example, given a set , the identity relation is defined as .

The identity relation is a specific type of equivalence relation that fulfills all the standard properties. Which is, for all , , and in the set ,

  • 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 is defined as

The identity function is bijective.

See Also