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

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

The number such as 8.5 , 2 3 and 4 1 3 room not integers.

(Note the a number can be an integer even if that is created as a decimal or a fraction: for example, − 3.00 and also 8 2 space both integers, due to the fact that they space equal to − 3 and also 4 , respectively.)

The collection of integers is usually stood for by the price .

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

We deserve to plot the integers together equally spaced clues on a number heat , as displayed in the figure. The arrows at the left and right sides display that the integers continue forever in both directions.

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The whole numbers better than 0 are called optimistic integers . Their opposites, i beg your pardon are much less than 0 , are referred to as an unfavorable integers . Zero is neither confident nor negative.

If 2 numbers room opposite, they room the same distance away from zero. Because that example, 4 and − 4 room opposites, and each is 4 units from zero.

The sum, difference, or product of two integers is an 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 that integers does not divide evenly, the an outcome is a portion .




You are watching: Set of whole numbers and their opposites

Example:

which of the complying with numbers is an integer?

6.5 , 5 , 2 3 , − 24

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

The number 5 has actually a square source sign; its worth is higher than the creature 2 but less than the essence 3 . Since 5 is no a perfect square favor 4 or 9 , 5 is not an integer.

The number 2 3 is a fraction greater 보다 0 but less than 1 , therefore 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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