# identity element

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Related to identity element: Inverse element

## 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.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 identity element - an operator that leaves unchanged the element on which it operates; "the identity under numerical multiplication is 1"operator - (mathematics) a symbol or function representing a mathematical operation
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
References in periodicals archive ?
Then (RNQ(H), [symmetry]) is a semi-hypergroup with identity element [bar.x] = (0, [p.summation over i=1] 0[T.sub.i], [r.summation over (j=1)] 0[I.sub.j], [s.summation over k=1] 0[F.sub.k]) if and only if (H, +) is a semi-hypergroup with identity element 0.
In view [6, theorem 2.5.1], if M is a W*-algebra and A [??] M is a commutative W*-subalgebra containing the identity element of M and d: M [right arrow] M a derivation, then there exists a [x.sub.0] [member of] M such that d(a) = a[x.sub.0] - [x.sub.0]a for each a [member of] A.
Let U be an open set of [K.sup.M.sub.l](C) containing the identity element and let V = [[PHI].sup.-1](U) [subset] [Comm.sub.l]C).
In the sequel, [absolute value of X] denotes the cardinality of a set X, Z the set of integers, [Z.sub.P] the set of integers satisfying a property P, and R a commutative Q-algebra with an identity element 1.
If (Eq.) is a group, then e denotes its identity element, and for a given (Eq.) and (Eq.) denote the left and the right translation by x, respectively.
The operation, for example, can be shown to be commutative (meaning that the order in which the minds are swapped doesn't affect the end result) but not associative, while considering what an identity element would look like could spawn some fruitful--and potentially philosophical--discussions.
The identity element will be denoted by 1 and the inverse of an element x will be denoted by [x.sup.-1].
Then m-ary semigroup (R, f) has an identity element 0 if
The identity element comes first, so the subgroup itself is listed first.
Suppose that G is a locally compact group, [omega] is a weight function on G bounded on a relatively compact open neighborhood U of the identity element of G, and 0 < p < 1.
Table 4 Components of Utilitarian and Normative Identities in Social Ventures Identity element Coding definition Utilitarian identity Growth Indication of a desire to expand or increase.

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