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/