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

The set of integers is usually represented by the symbol .

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

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.

Math diagram

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: ( 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 .

Example:

Which of the following numbers is an integer?

6.5 , 5 , 2 3 , 24

6.5 is greater than the integer 6 and less than the integer 7 . The .5 at the end of the number indicates a fractional part. So, this is not an integer.

The number 5 has a square root sign; its value is greater than the integer 2 but less than the integer 3 . Since 5 is not a perfect square like 4 or 9 , 5 is not an integer.

The number 2 3 is a fraction greater than 0 but less than 1 , so this is not an integer.

The number 24 is in the set { ... , 6 , 5 , 4 , 3 , 2 , 1 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , ... } .

So, 24 is an integer.

 

 

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