What is the meaning of identity?

noun

• The distinct personality of an individual regarded as a persisting entity.
  • usage: "you can lose your identity when you join the army"
  • synonyms: personal identity, individuality
• The individual characteristics by which a thing or person is recognized or known.
  • usage: "geneticists only recently discovered the identity of the gene that causes it"; "it was too dark to determine his identity"; "she guessed the identity of his lover"
• An operator that leaves unchanged the element on which it operates.
  • usage: "the identity under numerical multiplication is 1"
  • synonyms: identity element, identity operator
• Exact sameness.
  • usage: "they shared an identity of interests"
  • synonyms: identicalness, indistinguishability