Venn Diagram of Our Number System

Date: 12/13/2002 at 16:02:30
From: Ed Cramer
Subject: Venn Diagram of our Number System

I have learned that Real Numbers include counting numbers, whole 
numbers, integers, and rational and irrational numbers. With Real 
Numbers as the Universe I can (I think) draw a Venn diagram of this 
Universe, but I don't know how to include complex numbers that consist 
of a real part and and imaginary part. Can you please actually diagram 
this for me?   

Thank you ahead of time, 
Ed Cramer

Date: 12/13/2002 at 21:25:08
From: Doctor Peterson
Subject: Re: Venn Diagram of our Number System

Hi, Ed.

Here are a couple of pages on our site that diagram these relationships:

   Classifying Numbers
   http://mathforum.org/library/drmath/view/55736.html 

                           complex 
                            /   \
                   imaginary     real
                                /    \
                      irrational    rational
                                     /    \
                             integers      fractions
                                 |             |
                               whole        integers
                                 |
                             naturals

The following includes more types of numbers, and makes it more 
complicated than we want:

   Types of Numbers
   http://mathforum.org/library/drmath/view/52323.html 

Using the version above, we get this Venn diagram:

    +-------------------------------------------+
    |                  Complex                  |
    | +---------------------------------------+ |
    | |               Imaginary               | |
    | +---------------------------------------+ |
    |                                           |
    | +---------------------------------------+ |
    | | R             Irrational              | |
    | +-E-------------------------------------+ |
    | | A              Rational               | |
    | | L +--------------+-+--------------+   | |
    | |   |            Integer            |   | |
    | |   |              |Whole           |   | |
    | |   |              | |  Natural     |   | |
    | |   |              | |              |   | |
    | |   |  Negative    |0|  Positive    |   | |
    | |   +--------------+-+--------------+   | |
    | +---------------------------------------+ |
    +-------------------------------------------+

Note that there are complex numbers that are neither real nor 
imaginary (which answers your question), and rational numbers that are 
not integers, but all real numbers are either rational or irrational, 
and all integers are either positive, negative, or zero. Integers, 
whole numbers, and natural numbers are subsets of one another.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/