The ** integers ** are the collection of whole numbers and also their opposites. * fountain * and * decimals * space not consisted of in the set of integers.

for example, 2 , 5 , 0 , − 12 , 244 , − 15 and 8 are all integers.

The numbers such together 8.5 , 2 3 and also 4 1 3 room not integers.

(Note the a number have the right to be an integer even if it is written as a decimal or a fraction: because that example, − 3.00 and 8 2 room both integers, since they room equal to − 3 and 4 , respectively.)

The set of integers is usually stood for by the prize ** ℤ ** .

ℤ = ... , − 6 , − 5 , − 4 , − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , ...

We deserve to plot the integers as equally spaced point out on a number line , as shown in the figure. The arrows at the left and right sides show that the integers proceed forever in both directions.

The whole numbers greater than 0 are dubbed * positive integers * . Their opposites, i m sorry are less than 0 , are called * an adverse integers * . Zero is neither positive nor negative.

If two numbers are opposite, they room the exact same distance far from zero. For example, 4 and − 4 are opposites, and also each is 4 units from zero.

The sum, difference, or product of 2 integers is one integer. Because that example,

Sum: 3 + 4 = 7

Difference: 3 − 5 = − 2

Product: ( − 2 ) ( 3 ) = − 6

The quotient of 2 integers is not always an integer.

for example, 8 ÷ ( − 2 ) = − 4 is one integer due to the fact that it divides evenly.

However, − 2 ÷ 8 = − 2 8 = − 1 4 is not an integer. As soon as a quotient the integers does no divide evenly, the result is a * portion * .

You are watching: Set of whole numbers and their opposites

** Example: **

which of the following numbers is an integer?

6.5 , 5 , 2 3 , − 24

6.5 is better than the integer 6 and less 보다 the creature 7 . The .5 in ~ the finish of the number suggests a spring part. So, this is no an integer.

The number 5 has a square root sign; its value is higher than the creature 2 yet less 보다 the integer 3 . Since 5 is no a perfect square choose 4 or 9 , 5 is no an integer.

The number 2 3 is a fraction greater than 0 however less 보다 1 , for this reason 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 , ...

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