1
1.1 The Real Number System
Types of Numbers:
The following diagram shows the types of numbers that form the set of real numbers.
Definitions
1.
The
natural numbers
are the numbers used for counting.
1, 2, 3, 4, 5, . . .
A natural number is a
prime number
if it is greater than 1 and its only factors are 1 and itself.
A natural number is a
composite number
if it is greater than 1 and it is not prime.
Example: 5, 7, 13,29, 31 are prime numbers.
8, 24, 33 are composite numbers.
2.
The
whole numbers
are the natural numbers and zero.
0, 1, 2, 3, 4, 5, . . .
3.
The
integers
are all the whole numbers and their additive inverses.
No fractions or decimals.
. . . , 3, 2, 1, 0, 1, 2, 3, . . .
An integer is
even
if it can be written in the form
n
2
, where
n
is an integer (if 2 is a factor).
An integer is
odd
if it can be written in the form
1
2

n
, where
n
is an integer (if 2 is not a factor).
Example: 2, 0, 8, 24 are even integers and 1, 57, 13 are odd integers.