IB Mathematics HL Option Sets, relations and Groups - Identity element
The basic principles about identity element are:
- An element e in a set A is an identity element for an operation * defined over A if
e*x=x*e=x for every element
- If an operation * admits a left-identity
and a right-identity
, then these two identities are equal.
- If a binary operation * on a set A admits an identity element e, then this element is unique.
Concerning your question, suppose that the identity element is e, then
which is not unique, since is depending on x. So this operation has no identity.
Hope these help