Isn't 1/0 the Biggest Number?
Date: 02/28/98 at 10:21:40 From: Garrett Mason Subject: Isn't 1/0 the biggest number? Hi, Isn't 1/0 the biggest number? I mean it makes sense that if you add or multiply a number to the biggest number you will get the same biggest number, right? Okay, I'm going to add 9 to 1/0: 1 9 1 9*0 1 0 1 - + - = - + --- = - + - = - 0 1 0 1*0 0 0 0 Okay, now I'm going to multiply 1/0 by 5: 1 * 5 5 (which I'm told is the same as 1/0) - - = - 0 * 5 0 Is this correct? Thanks, Garrett
Date: 02/28/98 at 15:50:47 From: Doctor Sam Subject: Re: Isn't 1/0 the biggest number? Garrett, Your reasoning is excellent, but it is incorrect. I really like the way you reason that the biggest number can't be made larger. That is exactly the test for "biggest." The problem is not with your reasoning, it is with the way that you find a common denominator. By multiplying 9/1 by 0/0 to get 0/0 you are claiming that 9/1 = 0/0. But I could add 1/0 and 5/1 the same way to get: 1/0 + 5/1 = 1/0 + 5*0/1*0 = 1/0 + 0/0 = 1/0 But obviously 0/0 can't be equal to both 5 and 9! What you have actually discovered is that the ordinary rules of fractions don't work for 1/0 and 0/0 and for this reason mathematicians say that these symbols, although they look like ordinary fractions, don't really stand for anything. They aren't numbers. By the way, your second example doesn't really do what you want to do because 5/5 = 1. So you are really multiplying 1/0 by 1, so it isn't surprising that you get 1/0 as an answer. By the way, if you aren't convinced yet try repeating your first example by SUBTRACTING 9 (or anything else) from 1/0. Your method again gets 1/0 . . . but what it is true that the largest number can't be made larger, surely it can be made smaller? -Doctor Sam, The Math Forum Check out our web site http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.