The ** integers ** are the set of whole numbers and also their opposites. * fractions * and also * decimals * room not consisted of in the set of integers.

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

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

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

The set the 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 together equally spaced points on a number line , as displayed in the figure. The arrows in ~ the left and also right sides show that the integers proceed forever in both directions.

The entirety numbers better than 0 are dubbed * positive integers * . Your opposites, i beg your pardon are much less than 0 , are called * an adverse integers * . Zero is neither hopeful nor negative.

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

The sum, difference, or product of 2 integers is one integer. For 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 an integer because it divides evenly.

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

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** Example: **

i beg your pardon of the adhering to numbers is an integer?

6.5 , 5 , 2 3 , − 24

6.5 is greater than the integer 6 and less than the creature 7 . The .5 at the finish of the number suggests a fountain part. So, this is no an integer.

The number 5 has a square root sign; its value is higher than the integer 2 yet less than the creature 3 . Since 5 is not a perfect square prefer 4 or 9 , 5 is not an integer.

The number 2 3 is a portion greater 보다 0 however less than 1 , so 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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