Venn Diagram of Our Number SystemDate: 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/ |
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