Identity element

Therefore the number 0 is not considered an identity element for subtraction, even though x-0#61;x for all x, since 0-x#92;nex.

Proof. If e and e' are both identity elements, then we have ee'=e since e' is an identity element, and ee'=e' since e is an identity element. Thus e=ee'=e'.

Sometimes, to avoid ambiguity, we may use the notation e#95;M for the identity element of M. If multiplicative notation is used then we use the term identity element, and often use the notation 1, or 1#95;M, for the neutral element e.