INTEGERS

The following are properties of integers:

• Integers include both positive and negative whole numbers.

• Zero is considered an integer.

• Consecutive integers follow one another and differ by 1. For example, 6, 7, 8, and 9 are consecutive integers. Likewise, 0, −1, −2, and −3 are consecutive integers.

• The value of a number does not change when it is multiplied by 1 For example, 3 × 1 = 3.

The following are properties of real numbers:

REAL NUMBERS

• All real numbers correspond to points on the number line, as shown below:

• All real numbers except zero are either positive or negative. On a number line, such as that shown above, numbers that correspond to points to the right of zero are positive, and numbers that correspond to points to the left of zero are negative.

• For any two numbers on the number line, the number to the left is always less than the number to the right.

• Ordering is the process of arranging numbers from smallest to greatest or from greatest to smallest. The symbol > is used to represent “greater than,” and the symbol < is used to represent “less than.” To represent “greater than or equal to,” use the symbol ≥; to represent “less than or equal to,” use the symbol ≤.

• If any number n lies between 0 and any positive number x on the number line, then 0 < n < x; in other words, n is greater than 0 but less than x. If n is any number on the number line between 0 and any positive number x, including 0 and x, then 0 ≤ n ≤ x, which means that n is greater than or equal to 0 and less than or equal to x.

• If any number n lies between 0 and any negative number x on the number line, then − x < n < 0; in other words, n is greater than − x but less than 0. If n is any number on the number line between 0 and any negative number x, including 0 and − x, then − x ≤ n ≤ 0, which means that n is greater than or equal to − x and less than or equal to 0.