Download Real Numbers

Real Numbers
The Real Number System includes any number that
has a position on a number line.
Real numbers include natural numbers, whole numbers,
integers, rational numbers and irrational numbers.
Natural (or Counting) Numbers
N = {1, 2, 3, 4, 5,...}
Whole Numbers
{0, 1, 2, 3, 4, 5,...}
Whole numbers contain all the natural numbers, and
the number 0,
Integers
{..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,...}
Integers include all whole numbers and their opposites.
The natural numbers and the whole numbers are both
subsets of integers.
Rational Numbers
Rational Numbers include any number that can be
written in fraction form. For example
!7 which can be written as
-7
3
4
, or
are rational numbers.
1
Rational numbers also include decimals that are
terminating (come to an end) (1.56, -7.9) and
decimal numbers that are non-terminating and have a
repeated pattern of digits. ( For example (1.121 212
121…)
The natural numbers, whole numbers, and integers are
all subsets of rational numbers.
Irrational Numbers
An irrational number is a number that cannot be
written as a ratio of two integers (fraction). It
includes decimal numbers that are, non-terminating
and with digits that do not repeat in a fixed pattern.
Example—3.141 592 653 …
Looking at the diagram starting with natural numbers
you can see that:
• All whole numbers include all natural numbers.
Another way of saying this is that all natural
numbers are a subset of whole numbers. (They
are included in the set of whole numbers.)
• Natural numbers and Whole numbers are both
subsets of integers. (They are included in the
integer set)
• The natural numbers, whole numbers, and integers
are all subsets of rational numbers.