## Negative Numbers

You've probably run into situations which could be modeled by negative numbers: profits and losses, bank deposits and withdrawals, temperatures above and below freezing, buildings with elevators which go to floors above and below ground level, yardage gained and lost in football, and walking forward and backward.

Mathematicians define negative numbers as the opposites of positive numbers, since they are on the opposite side of zero from the positive numbers on a number line. Similarly, the opposites of the negative numbers are the positive numbers. The number 3 (negative three) is defined as the number which when added to +3 (positive three) equals zero. That is, 3 is the solution to the equation 3 + x = 0. The set of integers consists of all the whole numbers and their opposites. Zero is its own opposite. Those numbers which are greater than zero are positive and those numbers which are less than zero are negative. Zero is neither positive nor negative. Negative numbers are always written with a negative sign, but positive numbers may be written without a positive sign.

A common way to visualize integers is to use a number line like the one shown below. Here we can see that the numbers to the left of zero are negative and the ones to the right of zero are positive.

Placing Negative Numbers
on a Number Line