Zero over zero, how many numbers?
- To: mathgroup at smc.vnet.net
- Subject: [mg38951] Zero over zero, how many numbers?
- From: jwigner at redwood.cs.ttu.edu (Joe Wigner)
- Date: Wed, 22 Jan 2003 06:10:34 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
There seems to be some confusion on the terms undefined and indeterminate. First of all, karthik's statement that 0/0 cannot be indeterminate because it has to take the form (0x1)/0 is in error. That's just another name for 0/0. We could easily rewrite 0/0 in many different forms. Should we say that it is all numbers? Let's consider a different example: What is 6/2? Well, by reducing, we get 6/2=3. How do we know that is true? We can multiply 3 by 2 to get 6: 3*2=6. Now, let's apply that back to the original question. If we look at 0/0, what times zero gives us zero? 0*0=0, therefore 0/0=0 0*1=0, therefore 0/0=1 0*2=0, therefore 0/0=2 ... and on and on to the point any number can satisfy the question: What is 0/0? Now, is it undefined? Let's take a look at that. 6/0=undefined. Why? The answer is in the question we answered before. What multiplied by zero gives 6? The answer is, we don't know. There is noting defined to give us the number zero. 0/0 cannot be undefined because there are plenty of definitions for what it gives. It must therefore be indeterminate.