Integers

The integers are the set of whole numbers and their opposites. Fractions and decimals are not included in the set of integers.

For example, $2,5,0,-12,244,-15$ and $8$ are all integers.

The numbers such as $8.5,\frac{2}{3}$ and $4\frac{1}{3}$ are not integers.

(Note that a number can be an integer even if it is written as a decimal or a fraction: for example, $-3.00$ and $\frac{8}{2}$ are both integers, because they are equal to $-3$ and $4$ , respectively.)

The set of integers is usually represented by the symbol $\mathbb{Z}$ .

$\mathbb{Z}=\left\{\mathrm{...},-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,\mathrm{...}\right\}$

We can plot the integers as equally spaced points on a number line , as shown in the figure. The arrows at the left and right sides show that the integers continue forever in both directions.

The whole numbers greater than $0$ are called positive integers . Their opposites, which are less than $0$ , are called negative integers . Zero is neither positive nor negative.

If two numbers are opposite, they are the same distance away from zero. For example, $4$ and $-4$ are opposites, and each is $4$ units from zero.

The sum, difference, or product of two integers is an integer. For example,

Sum: $3+4=7$

Difference: $3-5=-2$

Product: $\left(-2\right)\left(3\right)=-6$

The quotient of two integers is not always an integer.

For example, $8÷\left(-2\right)=-4$ is an integer because it divides evenly.

However, $-2÷8=\frac{-2}{8}=-\frac{1}{4}$ is not an integer. When a quotient of integers does not divide evenly, the result is a fraction .