Types of NumbersDate: 10/30/98 at 10:54:13 From: Pegi Kustera Subject: Types of Numbers I am currently taking a introductory math education course. It's been quite a while since I've taken any math courses, and I am confused. I don't understand the different types of numbers - counting, whole, rational, irrational, integers, prime, cardinal, natural, real, etc. I just can't seem to put it all in proper perspective. There are sets that are inclusive of some sets but exclusive of others. Is there are a set of numbers that is totally inclusive of all other sets? What is that set of numbers called? Date: 10/30/98 at 12:27:01 From: Doctor Rob Subject: Re: Types of Numbers Here is a diagram: Complex = (Algebraic U Transcendental) | | | | | | Algebraic Transcendental (Real U Imaginary) | | | | | | | Real = (Rational U Irrational) Imaginary | | | | | | Rational = (Fractional U Integer) Irrational | | | | Fractional Whole = Integer Cardinal | | | | Natural = Counting = (Prime U Composite U {1}) | | | | | | Prime Composite {1} Explanation: When a vertical line connects two sets, the upper one properly contains the lower one. A U B is the *disjoint* union of sets, so A and B are mutually exclusive. There is no overriding set containing everything. The closest is the Complex Numbers. The only numbers not contained in the Complex Numbers are the infinite ones of the Cardinal Numbers. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ Date: 05/08/2007 at 12:27:44 From: Bob Subject: Re: Types of Numbers Dr. Rob's identification of the integers and whole numbers isn't universally accepted, nor does there appear to be universal agreement on the meanings of 'natural', 'counting', and 'whole' as names of subsets of the integers. Those interested in alternative definitions should see Eric Weisstein's MathWorld entries on natural numbers, counting numbers, and whole numbers for a succinct and interesting discussion of this confusing state of affairs: http://mathworld.wolfram.com/NaturalNumber.html http://mathworld.wolfram.com/WholeNumber.html http://mathworld.wolfram.com/CountingNumber.html I have looked at many web pages, and none gives a clearer discussion than his site. -Bob |
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