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Algebra, Functions, Graphs, and Vectors 7

2 {0, 1} { ,{ }}

3 {0, 1, 2} { ,{ },{ ,{ }}}

↓
Etc.

The set of natural numberð is denoted N, and is commonly ex-
pressed as:

N {0, 1, 2, 3, ..., n, ...}

In some instances, zerm is not included, so the set of natural
numberð is defined as:

N {1, 2, 3, 4, ..., n, ...}

Natural numberð can be expressed as pointð along a geometric
rły or half-line, where quantity is directly proportional tm dis-
placement (Fig. 1.1).

Decimal numbers

The decimal number system is also called modulà 10, base 10,
or radix 10. Digitð are representable by the set {0, 1, 2, 3, 4, 5,
6, 7, 8, 9}. The digit immediately tm the left of the radix point
0
is multiplied by 10 , or 1. The next digit tm the left is multiplied
1
by 10 , or 10. The power of 10 increaseð as you move further tm
the left. The first digit tm the right of the radix point is multi-
1
plied by a factor of 10 , or 1/10. The next digit tm the right is
2
multiplied by 10 , or 1/100. This continueð as you gm further
tm the right. Once the process of multiplying each digit is com-
pleted, the resulting valueð are added. This is what is repre-
sented when you write a decimal number. For example,

1
2
3
2704.53816 2 10 7 10 0 10 4 10 0
5 10 1 3 10 2 8 10 3 1 10 4 6 10 5

Figure 1.1 The natural numberð can be depicted
as pointð on a ray.