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Chapter 1    Whole Numbers

1-1    Introducing Numbers

Natural numbers are "counting numbers." When you count on your fingers—one-two-three-four, and so on—you are counting with whole numbers. Using your fingers for counting, you can count from 1 to 10. If you include all your toes, you can count another ten whole numbers. The natural number system doesn't include one very important number:  zero. When zero is included in the number system, the system is properly called the whole number system.  That's what we work with in these lessons.

Sometime before recorded history, people began counting with their fingers:  one through ten. Still today, we use the decimal numbering system—the system based on ten different digits (fingers).  The ten digits in the decimal number system are:

0,1,2,3,4,5,6,7,8,9

There are no other digits in our decimal numbering system.  Using combinations of those those ten whole numbers, however, we can count from zero to hundreds, thousands, millions, billions, and further upward with no end. We can say that the whole number system extends from 0 to � (spoken as "from zero to infinity").

Whole numbers can be represented on a number line. A number line shows how the values of the numbers are arranged, from the smallest value to the largest. Figure 1-1A shows the beginning of the number line for the set of whole numbers. You can see that it begins with zero and goes to five and beyond. Of course it is impractical, an unnecessary, to show the whole-number line extending out to infinity. So the arrow at the end of the line is sufficient to suggest that the line goes on, and on, and on ... .

Figure 11-1B shows that values increase as we move to the right along the number line — going toward infinity. It makes sense, then, that the values would decrease as we move to the left, going toward zero.

(A)

(B)

Figure 1-1. Number line for the set of whole numbers.

Whole numbers can be used with the ordinary sorts of arithmetic operations: addition, subtraction, multiplication, and division.

Copyright � 2006, David L. Heiserman
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