Definitions:

1. an operator that leaves unchanged the element on which it operates noun
   • the identity under numerical multiplication is 1
2. exact sameness noun
   • they shared an identity of interests
3. the distinct personality of an individual regarded as a persisting entity noun
   • you can lose your identity when you join the army
4. the individual characteristics by which a thing or person is recognized or known noun
   • geneticists only recently discovered the identity of the gene that causes it

Synonyms:

• identicalness
• identity element
• identity operator
• indistinguishability
• individuality
• personal identity