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## Definition of the noun Additive identity

What does Additive identity mean as a name of something?

noun

1. [algebra] An element of an algebraic structure, generally denoted 0, which is an identity for an additive operation (generally denoted +). That is, x + 0 = 0 + x = x for any x in the structure.

## Explanation

Additive identity: In mathematics the additive identity of a set which is equipped with the operation of addition is an element which, when added to any element x in the set, yields x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures where addition is defined, such as in groups and rings.

• also known as 加法單位元

## Printed dictionaries and other books with definitions for Additive identity

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### Math Dictionary With Solutions (1999)

by Chris Kornegay

> Additive Identity The additive identity is one of the properties of the real number system. It states that for any real number a there is a unique number 0 such that a +0 = a and 0+a = a. The number 0 is called the additive ...

### Blackie’s Dictionary of Mathematics

by Blackie

additive identity The number zero is called the additive identity because when we add it to a number say 'N', the result we get is the same number N. additive inverse ...

### Mathematics Illustrated Dictionary (2003)

Facts, Figures, and People by Jeanne Bendick

additive identity. In addition, the additive identity is zero. The sum of zero and any other number is the number itself. a+0=0+a=a See commutative property. additive inverse. a + (-a ) = (-a) + a ...

### The Relational Database Dictionary, Extended Edition (2008)

by Christopher Date

The elements 0 and 1 are called the additive identity and ...

### The New Relational Database Dictionary (2015)

Terms, Concepts, and Examples by C.J. Date

Those elements 0 and 1 are the additive identity and the multiplicative identity, respectively. Inverse laws: For all x in s, there exist elements −x and (unless x = 0) 1/x in s such that x+(−x) = 0 and ...

### Historical Encyclopedia of Natural and Mathematical Sciences (2009)

by Ari Ben-Menahem

x + 0 = x additive identity (ii ) x • 1 = x multiplicative identity (Hi) x + y = y + x \ , • , ,. \ ( commutative laws (iv) xy = yx } (v) (x + y} + z = x + (y + z} , . . , ; \ } . aj , . vy ' ) associative laws (vi) (xy)z = x( yz) (vii) x(ii + ...

### Dictionary of Classical and Theoretical Mathematics (2001)

by Catherine Cavagnaro, William T. Haight, II

The additive identity of an Abelian group A.

### CRC Concise Encyclopedia of Mathematics, Second Edition (2002)

by Eric W. Weisstein

Additive identity: There exists an ...

### MCGRAW-HILL DICTIONARY OF MATHEMATICS, 2/E (2002)

by McGraw-Hill Education

{ 'ad-ad-iv 'forJ-shen} additive identity In a mathematical system with an operation of addition ...

## Online dictionaries and encyclopedias with entries for Additive identity

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