nonidentity

noun

1. Difference, distinction; failure to be identical.

   “No scientific examiner would select only chance variations to establish nonidentity of two specimens when the fundamental points of identification stamp them as originating at a single source.”

2. An operator which modifies its operand, and which therefore is not the identity.

   “Moreover, in a group of prime order p, every non-identity element (i.e. every element other than 1) has period p.”