# 0/0 = ?

1. Apr 7, 2005

### Euphoriet

Sorry I cant seem to find a 'constant" answer anywhere..

2. Apr 7, 2005

### chroot

Staff Emeritus
0/0 is indeterminate. It has no specific value.

- Warren

3. Apr 7, 2005

### mattmns

Undefined, afaik.

4. Apr 7, 2005

### Data

Indeterminate. It doesn't mean the same thing as "undefined."

If you have real numbers $a$ and $b\neq 0$ then we say

$$\frac{a}{b} = c$$

if

$$a = bc$$

Now, say $a=b=0$ so we are looking at $0/0$. But $0 = 0c$ is true for every real c, so we can't give it a specific value. We thus call it "indeterminate."

5. Apr 7, 2005

### Hurkyl

Staff Emeritus
Undefined. It doesn't mean the same thing as "indeterminate". :tongue2:

When a value z is not in the domain of a function f, we say that f is undefined at z, or more simply, f(z) is undefined.

This is exactly what's going on here: (0, 0) is not in the domain of the binary function /.

The only mathematical usage of the term "indeteriminate" that I can recall is that of an indeterminate form. The particular relevant example is when you have a limit of a ratio, and you naively apply the limit theorems to get the fraction 0/0, this is said to be an indeterminate form. This is not because you're trying to evaluate 0 divided by zero, but because your manipulations have not provided you with any useful information about the limit.

Last edited: Apr 7, 2005
6. Apr 7, 2005

### Moonbear

Staff Emeritus
Well, I'm glad everyone agrees. :rofl:

7. Apr 7, 2005

### Danger

Do I detect the initial stages of a hijacking?

8. Apr 7, 2005

### Hurkyl

Staff Emeritus
Thou mocketh us?

9. Apr 7, 2005

### Data

You're right... I should say that it is both undefined and indeterminate, with the qualification that the term indeterminate refers to some subclass of things that are undefined (although I haven't thought about precisely how I would want to define this subclass, and in this case I should say that it is undefined and more precisely indeterminate). Obviously using indeterminate in that way does not put it in any sort of direct correlation with the notion of an indeterminate form.

Note that I have carefully constructed this such that nothing in my last post is quite untrue. :tongue2:

I like being able to define things~

Last edited: Apr 7, 2005
10. Apr 7, 2005

### Moonbear

Staff Emeritus
Moi?

All I know is that winding up with 0/0 either meant I needed to go back and find the mistake in my math homework, or that I've included the wrong cells in Excel in my formula for something.

11. Apr 7, 2005

### cronxeh

*puts his hand on Moonbear's shoulder*

easy.. easy.. RUN! RUN BIOLOGY GURU RUN!! :rofl:

12. Apr 8, 2005

### Moonbear

Staff Emeritus
Phew! Narrow escape! Thanks. :uhh: Wait, how did I wind up back in this thread?! *ducks and runs* What did I do with that kevlar apron?

13. Apr 8, 2005

### franznietzsche

Of course. What else would she do?

14. Apr 8, 2005

### Moonbear

Staff Emeritus
:uhh: *sprays around more pheromones*

How about we call it indeterminately undefined? (How's that for diplomacy?) :rofl:

15. Apr 8, 2005

### cronxeh

*looks over to the left*

I think you've angered the angry Quantum Physics mob!

16. Apr 8, 2005

### franznietzsche

:yuck:

Are you sure that wasn't the rhino spray?

17. Apr 8, 2005

### Moonbear

Staff Emeritus
Oops, I think that was the experimental tibbet spray.

18. Apr 8, 2005

### franznietzsche

Is his head supposed to do that?!?!

19. Apr 8, 2005

### Smurf

This is quite cool, I'm gonna have to remember this.
So.... In other words an imprecise imprecision?

20. Apr 8, 2005

### Moonbear

Staff Emeritus
Meh, I'm not worried about the Quantum Physics mob, I've got the Genco families backing me. :tongue2:

Well, we have established that Euphoriet is right, he can't get a constant answer anywhere. (BTW, Euphoriet, if you're looking for a correct answer, ignore me over here...this is what you get for asking a math question in GD).