The ** integers ** are the collection of whole numbers and their opposites. * fractions * and also * decimal * room not contained 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 space not integers.

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

The set of integers is usually represented by the price ** ℤ ** .

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

We have the right to plot the integers together equally spaced points on a number heat , as presented in the figure. The arrows in ~ the left and right sides display that the integers continue forever in both directions.

The whole numbers greater than 0 are referred to as * hopeful integers * . Your opposites, i m sorry are less than 0 , are called * an adverse integers * . Zero is neither hopeful nor negative.

If two numbers room opposite, they are the same distance far from zero. Because that example, 4 and − 4 room opposites, and also each is 4 systems 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 constantly an integer.

because that 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 of integers does no divide evenly, the an outcome is a * portion * .

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** Example: **

which of the following numbers is an integer?

6.5 , 5 , 2 3 , − 24

6.5 is better than the creature 6 and also less 보다 the integer 7 . The .5 at the finish of the number indicates a fractional part. So, this is not an integer.

The number 5 has actually a square root sign; its worth is better than the creature 2 yet less than the creature 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 than 0 yet 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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