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identity

[ahy-den-ti-tee, ih-den-]
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noun, plural i·den·ti·ties.
  1. the state or fact of remaining the same one or ones, as under varying aspects or conditions: The identity of the fingerprints on the gun with those on file provided evidence that he was the killer.
  2. the condition of being oneself or itself, and not another: He began to doubt his own identity.
  3. condition or character as to who a person or what a thing is; the qualities, beliefs, etc., that distinguish or identify a person or thing: a case of mistaken identity; a male gender identity; immigrants with strong ethnic identities.
  4. the state or fact of being the same one as described.
  5. the sense of self, providing sameness and continuity in personality over time and sometimes disturbed in mental illnesses, as schizophrenia.
  6. exact likeness in nature or qualities: an identity of interests.
  7. an instance or point of sameness or likeness: to mistake resemblances for identities.
  8. Logic. an assertion that two terms refer to the same thing.
  9. Mathematics.
    1. an equation that is valid for all values of its variables.
    2. Also called identity element, unit element, unity.an element in a set such that the element operating on any other element of the set leaves the second element unchanged.
    3. the property of a function or map such that each element is mapped into itself.
    4. the function or map itself.
  10. Australian Informal. an interesting, famous, or eccentric resident, usually of long standing in a community.
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Origin of identity

1560–70; < Late Latin identitās, equivalent to Latin ident(idem) repeatedly, again and again, earlier *idem et idem (idem neuter of īdem the same + et and) + -itās -ity
Related formsnon·i·den·ti·ty, noun

Synonyms

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5. individuality, personality, distinctiveness, uniqueness.
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018
British Dictionary definitions for identity element

identity

noun plural -ties
  1. the state of having unique identifying characteristics held by no other person or thing
  2. the individual characteristics by which a person or thing is recognized
  3. Also called: numerical identity the property of being one and the same individualhis loss of memory did not affect his identity
  4. Also called: qualitative identity the state of being the same in nature, quality, etcthey were linked by the identity of their tastes
  5. the state of being the same as a person or thing described or claimedthe identity of the stolen goods has not yet been established
  6. identification of oneself asmoving to London destroyed his Welsh identity
  7. logic
    1. that relation that holds only between any entity and itself
    2. an assertion that that relation holds, as Cicero is Tully
  8. maths
    1. an equation that is valid for all values of its variables, as in (x – y)(x + y) = x ² – y ². Often denoted by the symbol ≡
    2. Also called: identity elementa member of a set that when operating on another member, x, produces that member x: the identity for multiplication of numbers is 1 since x .1 = 1. x = xSee also inverse (def. 2b)
  9. Australian and NZ informal a well-known person, esp in a specified locality; figure (esp in the phrase an old identity)
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Word Origin

C16: from Late Latin identitās, from Latin idem the same
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Word Origin and History for identity element

identity

n.

c.1600, "sameness, oneness," from Middle French identité (14c.), from Late Latin (5c.) identitatem (nominative identitas) "sameness," from ident-, comb. form of Latin idem (neuter) "the same" (see identical); abstracted from identidem "over and over," from phrase idem et idem. [For discussion of Latin formation, see entry in OED.] Earlier form of the word in English was idemptitie (1560s), from Medieval Latin idemptitas. Term identity crisis first recorded 1954. Identity theft attested from 1995.

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Online Etymology Dictionary, © 2010 Douglas Harper
identity element in Medicine

identity

(ī-dĕn′tĭ-tē)
n.
  1. The set of behavioral or personal characteristics by which an individual is recognizable as a member of a group.
  2. The distinct personality of an individual regarded as a persisting entity; individuality.
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The American Heritage® Stedman's Medical Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
identity element in Science

identity element

[ī-dĕn′tĭ-tē]
  1. The element of a set of numbers that when combined with another number under a particular binary operation leaves the second number unchanged. For example, 0 is the identity element under addition for the real numbers, since for any real number a, a + 0 = a, and 1 is the identity element under multiplication for the real numbers, since a X 1 = a.
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The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.