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Integers

Theintegersare the set ofwhole numbersand their opposites.Fractionsanddecimalsare 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.)

Thesetof 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 anumber 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 calledpositive integers. Their opposites, which are less than$0$, are callednegative 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 afraction.