Numbers between 0 and 9999Date: 7/15/96 at 21:48:43 From: Lucas W Tolbert Subject: How Many Numbers.... My Dad and I were arguing last night. I said there were only 10000 whole numbers counting zero between 0 and 9999 but he said there are an infinite number. I know I am right but he wants me to ask what you think. Date: 7/15/96 at 22:18:32 From: Doctor Sydney Subject: Re: How Many Numbers.... Dear Lucas, You were right! Whole numbers are the numbers we count with: 1, 2, 3, ... One way to define a whole number is that if you were to write a whole number in the form of a fraction, where it is reduced as far as possible (meaning there are no common divisors in the numerator and the denominator), there would be a 1 in the denominator. So, the only whole numbers between 0 and 9999 inclusive are: 0, 1, 2, 3, ..., 9998, 9999. However, there ARE an infinite number of RATIONAL numbers and REAL numbers between 0 and 9999. A rational number is a number that can be written as a fraction where the numerator and denominator are positive or negative whole numbers, and a real number is any number that you can find on the number line, whether it be a rational number like 1/2 or an irrational number like pi. Infinity has some strange, interesting properties. For instance, it turns out that the number of real numbers between 0 and 9999 is the same as the number of real numbers between 0 and 1! What's more, mathematicians have defined several different "sizes" of infinity. So, the infinity associated with the rational numbers between 0 and 1 is "smaller" than the infinity associated with the real numbers between 0 and 1. However, the total number of whole numbers ({1, 2, 3,..., 9999, 10000, ...}) is the same "size" as the number of rational numbers between 0 and 1. As you can see, problems dealing with infinity can be tricky and surprising, but they can turn out to be pretty fun! If you want to learn more about the different "sizes" of infinity or any other questions you have about infinity, please do write back! We love infinity (or at least I do)! Hope I was able to help in the dispute and hope it has a peaceful resolution! :) -Doctor Sydney, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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