We have seen that the number line extends to the right from zero. It also
extends to the
left from zero. However, the set of numbers defined by
the term whole numbers includes only positive numbers, those pictured in the
number line above. The set of whole numbers does
not include negative
numbers, which extend to the left from zero on the number line below. This
second number line is called an integer number line, since integers are the
set of numbers including all whole numbers and their negative opposites. Two
opposite numbers are the same distance from zero on the number line, but on
opposite sides. For example, 3 and
-3 are opposites. 0 does not have an
opposite.
Figure 1.2: Integer Number Line
On the integer number line, each number is still greater than all the numbers to
its left and less than all the numbers to its right. Thus, we can see that 2
and 5 are greater than
-3 and
-3 is greater than
-4.
All positive numbers are greater than all negative numbers. Plus, if one
positive number is greater than another positive number, then its opposite is
less than the opposite of the other number. For example, 5 is greater than 3 (5
is to the right of 3), but -5 is less than -3 (-5 is to the left of -3). Two opposites, as you might expect, will cancel each other out; when added together they will equal 0.
