The Real Number System in a Venn Diagram
Date: 09/08/98 at 22:53:02 From: Amy Subject: The real number system My PreCal teacher gave us an assignment on the first day to construct a Venn diagram that illustrates the real number system. I have no idea where to begin and was hoping you could at least identify all the parts of the real number system for me and how they relate to each other so I can at least have some reference. Thank you.
Date: 09/08/98 at 23:17:47 From: Doctor Margaret Subject: Re: The real number system Hi Amy, Thanks for writing to Dr. Math. I'll give you an explanation of the real numbers first: Real numbers are in a set made up of all different kinds of numbers. First we have the natural numbers, or counting numbers, such as: 1, 2, 3, ... Then we have numbers where addition and multiplication will always result in a natural number, but these numbers alone are not sufficient for subtraction, as in the case of 3 - 9, or 1 - 1. So we have to add zero and negative whole numbers to our collection, and they are called integers: ..., -3, -2, -1, 0, 1, 2, 3, ... Now we have enough numbers for addition, multiplication, and subtraction, but not for division, so we need other numbers called ratios of integers, better known as fractions: 1/2, 2/3, 34/37, etc. All these numbers together, the natural numbers, integers, and ratios of integers are known as rational numbers. Rational numbers generally produce other rational numbers when they are added, multiplied, subtracted, or divided, but not always. For example, in the equation x^2 - 2 = 0, when we solve for x, we get x^2 = sqrt 2. This is irrational because it doesn't work out to something neat like x^2 = sqrt 9, which is x = 3. Sqrt 2 is a non-repeating, non-terminating decimal. So are numbers like Pi and e. We call all numbers of this type irrational. So real numbers are made up of all rational and irrational numbers. No number can be both rational and irrational, so you will have at least two separate circles for your diagram. There is a really good description of how to do a Venn diagram at: Venn Diagrams http://mathforum.org/library/drmath/view/52420.html Good luck! - Doctor Margaret, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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