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identity element

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identity element

 
Use identity element in a Sentence
–noun Mathematics.
identity (def. 9b).
Origin:
1900–05

i⋅den⋅ti⋅ty

  [ahy-den-ti-tee, i-den-]
–noun, plural -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 doubted his own identity.
3. condition or character as to who a person or what a thing is: a case of mistaken identity.
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.
a. an equation that is valid for all values of its variables.
b. 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.
c. the property of a function or map such that each element is mapped into itself.
d. the function or map itself.
10. Australian Informal. an interesting, famous, or eccentric resident, usually of long standing in a community.
Origin:
1560–70; < LL identitās, equiv. to L ident(idem) repeatedly, again and again, earlier *idem et idem (idem neut. of īdem the same + et and) + -itās -ity

Synonyms:
5. individuality, personality, distinctiveness, uniqueness.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2009.
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identity element  
n.  The element of a set of numbers that when combined with another number in a particular operation leaves that number unchanged. For example, 0 is the identity element under addition for the real numbers, since if a is any real number, a + 0 = 0 + a = a. Similarly, 1 is the identity element under multiplication for the real numbers, since a × 1 = 1 × a = a. Also called unity.
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Word Origin & History

identity 
1570, from M.Fr. identité (14c.), from L.L. (5c.) identitatem (nom. identitas) "sameness," from ident-, comb. form of L. idem (neut.) "the same" (see identical); abstracted from identidem "over and over," from phrase idem et idem. Term identity crisis first recorded 1954.
Online Etymology Dictionary, © 2001 Douglas Harper
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Legal Dictionary

Main Entry: iden·ti·ty
Function: noun
Inflected Form: plural -ties
1 : sameness of essential character or aspect identity of the issues and the parties>
2 a : separate or distinct existence identity or become an integral part of the immovable —Louisiana Civil Code> b : distinguishing character of a person; especially : information (as a name or address) that distinguishes a person identity of an informer> identity of the proper party —Federal Rules of Civil Procedure Rule 15(c)>
3 : the condition of being the same as a thing or person described, claimed, or accused identity of a crime's perpetrator>
Merriam-Webster's Dictionary of Law, © 1996 Merriam-Webster, Inc.
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Medical Dictionary

Main Entry: iden·ti·ty
Pronunciation: I-'den(t)-&t-E, &-'
Function: noun
Inflected Form: plural -ties
1 : the distinguishing character or personality of an individual
2 : the relation established by psychological identification
Merriam-Webster's Medical Dictionary, © 2002 Merriam-Webster, Inc.
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Medical Dictionary

identity i·den·ti·ty (ī-děn'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.

The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
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