Additive identity is a fundamental concept in mathematics that plays a crucial role in defining the properties of numbers, operations, and algebraic structures. It is a concept that is used in many different areas of mathematics, including arithmetic, algebra, and calculus. In this article, we will explore the definition and meaning of additive identity in detail.

## Definitions

Additive identity is a mathematical concept that refers to the number that, when added to any other number, leaves the number unchanged. In other words, it is the number that does not change the value of the number it is added to. The additive identity is denoted by the symbol 0.

## Origin

The concept of additive identity has been around since ancient times. The Babylonians and Egyptians used a zero-like symbol to represent the concept of nothingness. The Greeks used the word “μηδέν” (medén) to represent the concept of zero. The modern concept of additive identity was developed by mathematicians in the 19th century.

## Meaning in different dictionaries

Additive identity is defined in various dictionaries as the number that, when added to any other number, leaves the number unchanged. It is also defined as the number that does not change the value of the number it is added to.

## Associations

Additive identity is closely associated with the concept of addition. It is an essential property of addition and is used to define many other properties of numbers and algebraic structures. It is also used in many different areas of mathematics, including arithmetic, algebra, and calculus.

## Synonyms

The synonyms of additive identity include the following:

- Identity element.
- Neutral element.
- Zero element.

## Antonyms

The antonyms of additive identity include the following:

- Non-identity element.
- Non-neutral element.
- Non-zero element.

## The same root words

The same root words of additive identity include the following:

- Additive inverse.
- Additive property.
- Additive operation.
- Additive group.

## Example Sentences

Here are some example sentences that use the concept of additive identity:

- The additive identity of the set of real numbers is 0.
- The additive identity of the set of integers is 0.
- The additive identity of the set of complex numbers is 0 + 0i.
- The additive identity of the set of matrices is the zero matrix.
- The additive identity of the set of polynomials is the polynomial with all coefficients equal to 0.