The ** integers ** are the set of whole numbers and also their opposites. * fractions * and * decimal * space not included in the set of integers.

because that example, 2 , 5 , 0 , − 12 , 244 , − 15 and 8 room all integers.

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

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

The set the integers is usually represented by the prize ** ℤ ** .

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 proceed forever in both directions.

The whole numbers better than 0 are dubbed * optimistic integers * . Their opposites, i beg your pardon are much less than 0 , are called * negative integers * . Zero is neither positive nor negative.

If 2 numbers space opposite, they are the exact same distance far from zero. Because that example, 4 and also − 4 are opposites, and also each is 4 devices from zero.

The sum, difference, or product of 2 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.

because that example, 8 ÷ ( − 2 ) = − 4 is one integer because it divides evenly.

However, − 2 ÷ 8 = − 2 8 = − 1 4 is not an integer. Once a quotient the integers does not divide evenly, the result is a * fraction * .

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** Example: **

i m sorry of the following numbers is one integer?

6.5 , 5 , 2 3 , − 24

6.5 is higher than the creature 6 and also less 보다 the essence 7 . The .5 in ~ the end of the number shows a spring part. So, this is no an integer.

The number 5 has actually a square source sign; its worth is better than the integer 2 yet less than the integer 3 . Because 5 is not a perfect square choose 4 or 9 , 5 is no an integer.

The number 2 3 is a portion greater 보다 0 however less 보다 1 , therefore this is not an integer.

The number − 24 is in the collection ... , − 6 , − 5 , − 4 , − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , ...

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