Natural Numbers(N):
Natural Numbers are counting numbers from 1,2,3,4,5,................
N = {1,2,3,4,5,................}
Whole Numbers (W):
Whole numbers are natural numbers including zero. They are 0,1,2,3,4,5,...............
W = {0,1,2,3,4,5,..............}
W = 0 + N
Positive Numbers:
Positive numbers are, 1,2 ,3 ,4 ,5.................
Positive Numbers: {1, 2, 3, . . .}
Negative Numbers:
Negative numbers are, ............3, 2, 1.
Negative integers: { . . . 3, 2, 1}
Integers (Z):
 Whole Numbers together with negative numbers.
 Integers are set containing the positive numbers, 1, 2, 3, 4, ...., and negative numbers,............3, 2, 1, together with zero.
 Zero is neither positive nor negative, but is both.
 In other words, Integers are defined as set of whole numbers and their opposites.
 Z = {..., 3, 2, 1, 0, 1, 2, 3, .....}
Rational Numbers (Q):
 All numbers of the form , where a and b are integers (but b cannot be zero)
 Rational numbers include fractions:
* Proper Fraction: Numbers smaller than 1 eg: 1/2 or 3/4
* Improper Fraction: Numbers greater than 1 eg: 5/2
* Mixed Fraction: 2 1/2 = 5/2
 Powers and square roots may be rational numbers if their standard form is a rational number.
 In rational numbers the denominator cannot be zero
Example:
2 can be expressed in the form of p/q as 2/1
13/9 = 1.444.......
8^{2} = 0.015625
(√16)/3 = 4/3 = �1.333...
�4 = 2
1/2 = 0. 5  Rational (terminates)
2/3 = 0.6666666.......Rational (repeats)
5/11 = 0.454545......Rational (repeats)
Irrational Numbers Q^{1}:
 Cannot be expressed as a ratio of integers.
 As decimals they never repeat or terminate (rationals always do one or the other)
 They go on for ever or infinity.
Example: �2, �3, �7, �8
square root of 2 = �2 = 1. 41421356......Irrational (never repeats or terminates)
pi = p = 22/7 = 3.14159265....... Irrational (never repeats or terminates)
Real Numbers R:
 Real Numbers are every number, irrational or rational.
 Any number that you can find on the number line.
 It is a number required to label any point on the number line; or it is a number that names the distance of any point from 0.
 R = Q + Q^{1}
 Natural Numbers are Whole Numbers, which are Integers, which are Rational Numbers, which are Real Numbers.
 Irrational Numbers are Real Numbers, but not all Real Numbers are Irrational Numbers.
Examples:
 
0.45  rational real 
3.1415926535...................  irrational, real 
3.14159  rational, real 
0  whole, integer, rational, real 
5/3  rational, real 
1 2/3 = 5/3  rational, real 
�2 = 1. 41421356......  irrational, real 
�81 = 9  integer, rational, real 
9/3  rational, real 
�25 = 5  natural, whole, integer, rational, real 
9/3 = 3  natural, whole, integer, rational, real 
3/4  rational, real 
p = 3.1428571...  irrational, real 
3.144444.......  rational, real (since it is a repeating decimal)

Directions: Choose the correct answer. Also, write five examples of your own for each type of number.
