# Additive identity

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## Definition of the noun Additive identity

What does Additive identity mean as a name of something?

**noun**

- [
*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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## Video about Additive identity

**Additive identity Meaning**

Video shows what additive identity means. An element of an algebraic structure, generally denoted 0, which is an identity for an additive operation (generally ...