Re: Zero over zero, how many numbers?
- To: mathgroup at smc.vnet.net
- Subject: [mg38979] Re: Zero over zero, how many numbers?
- From: atelesforos at hotmail.com (Orestis Vantzos)
- Date: Thu, 23 Jan 2003 08:05:03 -0500 (EST)
- References: <b0lv6k$59o$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I don't really see the point in all this, but here is my opinion: 0/0 is indeterminate and not undefined because it can NOT be defined! It is in a sense 'undefinable', hence indeterminate. If you don't know anything about complex numbers, it appears to you that Sqrt[-1] has no meaning, just as 0/0. It is not the same though: Sqrt[-1] can be defined to have a single (non-real) value I, so that the whole construct that results has an internal consistency. Since it can actually be defined, it is undefined(if you stick to real numbers) and not indeterminate. 0/0 is indeterminate for exactly the opposite reason: if someone tries to give it a reasonable value, it can be proven that ANY number would be equal to it and the resulting construct would collapse immediately. Therefore 0/0 is indeterminate, eg. undefinable. Orestis Vantzos jwigner at redwood.cs.ttu.edu (Joe Wigner) wrote in message news:<b0lv6k$59o$1 at smc.vnet.net>... > 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.