# What are Integers?

May 31, 2015

Integers are counting numbers $\left\{1 , 2 , 3 , \ldots\right\}$, zero ($0$) and negative versions of counting numbers $\left\{- 1 , - 2 , - 3 , \ldots\right\}$.

Some nice properties of the integers ($\mathbb{Z}$) under addition ($+$) are as follows:

$n + 0 = n$ for all integers $n$.

If $m$ and $n$ are integers, then $m + n$ is an integer.

If $n$ is an integer then there is an integer $m$ such that $n + m = 0$.

In short, the integers are an example of a group under addition.

Nov 15, 2017

An integer can be defined as a whole number that is not a decimal or fraction, just the number itself

Nov 15, 2017

An integer is a whole number (Ex: 1, 5, 100)

#### Explanation:

An integer is a whole number that can be positive, negative, or zero. It cannot be a fraction.

Example:

Integers: -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
NOT integers: 1/2, 0.33, $\sqrt{2}$