# Additive identity

On this page:

## 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

Click on a title to look inside that book (if available):

### 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 The opposite of
a ...

### The Concise Oxford Dictionary of Mathematics (2014)

by Christopher Clapham, James Nicholson

**additive identity** The identity element under an operation of addition,
usually denoted by 0, so aþ01⁄40þa 1⁄4a. additive inverse See inverse element.
adherent point A point of the *closure of a set. ad infinitum Repeating infinitely ...

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

by Eric W. Weisstein

**Additive identity**: There exists an element 0 S such that for all a S : 0'a0a'00a; / 4.

### Concise Dictionary of Mathematics (2012)

**Additive Identity** Property For any number a, a + 0 = 0 + a In words, adding zero to
a number leavesthe numberunchanged, hence the “identical” number. Algebra A
language that helps translate reallife situations into mathematical form so that ...

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

by Christopher Date

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

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

by Catherine Cavagnaro, William T. Haight, II

**The additive identity** of an Abelian group A. The element denoted as 0 e A which
...

### Concept S Dictionary Of Agricultural Sciences (1992)

by I. C. Gupta, S. K. Gupta

Zero **The additive identity** element of an algebraic system. Zero-access storage
Computer storage for which waiting time is negligible. Zero adjuster A device for
adjusting the pointer position of an instrument or metre to read zero when the ...

### Encyclopedia of Cryptography and Security (2014)

by Henk C.A. van Tilborg, Sushil Jajodia

**The additive identity** 0 does not have a multiplicative inverse. Then (S*, ><) is a
group with respect to the multiplication operation; it is called the multiplicative
group of the ring, or sometimes the group of units. Nonzero elements x for which
...

## Online dictionaries and encyclopedias with entries for Additive identity

Click on a label to prioritize search results according to that topic:

## 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 ...