Download Number Systems Definitions

Number Systems
Every number you can imagine can be classified as a certain type of number. A number may belong to one or
more of the sets listed below.
The Natural Numbers (abbreviated N) are the set of numbers {1,2,3,4,5……}. These are sometimes called the
counting numbers, as they are the first numbers children learn to count with.
The Whole Numbers (abbreviated W) are the set of numbers {0,1,2,3,4,5……}. The Whole Numbers include the
Natural Numbers plus the number zero. You can remember this set by thinking that this set is the first set to
include the number with the hole in it (zero). (Hole… Whole, get it?  )
The Integers (abbreviated I) are the set of numbers {…-3,-2,-1,0,1,2,3……}. The Integers include the positive
and negative Natural Numbers, plus the number zero.
m
A Rational Number (abbreviated Q) can be expressed as a ratio
, where m and n are Integers and n is not zero.
n
The Rational Numbers are abbreviated with “Q” because each number in this set can be written as a quotient.
The decimal form of a Rational Number is either a terminating or repeating decimal. Examples include
2
, 1.23, 5.8,  7, 0 . The Natural Numbers, Whole Numbers and Integers are subsets of the Rational
3
Numbers.
Any Real Number that is not a Rational Number is an Irrational Number (abbreviated Ir or Irr). Examples
include 2 , π, 7 . (Note: any number that is not a perfect square has an irrational square root.)
Each Real Number (abbreviated  ) corresponds to exactly one point on the number line, and every point on
the number line represents exactly one real number. Every Real Number can be classified as Rational or
Irrational.
The Venn Diagram below shows the relationship between all these sets of numbers.
Real Numbers
() 
Q
Irrational
Numbers
(Ir)
I
W
N
Examples
For each number listed below, the number systems to which it belongs is listed.
1
N, W, I, Q, 
0
W, I, Q, 
-10
I, Q, 
0.5
Q, 
Ir, 
10
N, W, I, Q, 
36
belongs to none of the number systems listed
-9
above (Imaginary Number – used in Algebra II
and higher Math classes)