Synonyms for Identity (same or very similar meaning)
WordNet sense 1 (an operator that leaves unchanged the element on which it operates):
identity element, identity operator
WordNet sense 2 (exact sameness):
identicalness, indistinguishability
WordNet sense 3 (the distinct personality of an individual regarded as a persisting entity):
individuality, personal identity
From the ODE community, based on WordNet
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