Arithmetic : Real Numbers

Positive and Negative Numbers

Any real number except 0 (zero) is either negative or positive.
Numbers to the left of 0 on the number line are negative numbers.
Negative numbers are written with a minus sign (e.g., −5).
Numbers to the right of 0 on the number line are positive numbers.
Positive numbers may be written with a plus sign (e.g., +5), but usually the plus sign is omitted (e.g., 5).
Thus, real numbers may be referred to as signed numbers.
Signed numbers are useful to understand physical concepts.
For example, a loss of $50 can be represented by −$50 and a profit of $50 by +$50.

On the number line, numbers are ordered with a number to the left is less than a number to the right.
For example, −5 < −4 < −3, −2 < −1.5 < −1 and 1 < √3 < 2.
Note that 1 < n < 2 means n > 1 and n < 2 (i.e., number n is between 1 and 2 on the number line).
Similarly, 1 ≤ n ≤ 2 means n ≥ 1 and n ≤ 2 (i.e., number n is between 1 and 2, inclusive).