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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, 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 8/2 are both integers, because they are equal to –3 and 4, respectively.)

The set of integers is usually denoted by the symbol Z .

Z = {..., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, ...}

The integers are often represented as equally spaced points on a number line, as shown in the figure, continuing forever in both directions, as indicated by the arrows.

The whole numbers greater than 0 are called positive integers and their opposites are less than 0 and are called negative integers . Zero is neutral and it 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: (–2)(3) = –6

The quotient of two integers is not always an integer.

For example, 8 ÷ (–2) = –4 is an integer because it divides evenly.

However, –2 ÷ 8 = –2/8 = –1/4 is not an integer. When a quotient of integers does not divide evenly, the result is a fraction , also known as a rational number.