# Division by zero

1. Aug 15, 2012

### sambarbarian

In most cases division be zero ends up with not defined , but why do people sometimes call it infinity ?

2. Aug 15, 2012

### ImaLooser

Maybe they are being loose. It seems like a bad idea to me.

3. Aug 15, 2012

### Diffy

You should probably read the FAQs.

Look. Dividing by 0 is not defined in the Real numbers. PERIOD.

People who call it infinity are either,

1) Don't know what they are talking about and are wrong.

-or-

2) Doing very high level math, using a different number system.

4. Aug 15, 2012

### Mute

Or 3), they are being loose with terminology and mean it in a limit sense, e.g., $\lim_{x \rightarrow 0^+} 1/x = \infty$

5. Aug 15, 2012

### arildno

Infinity is not a defined number within the reals..

6. Aug 15, 2012

### sambarbarian

i think that's it

7. Aug 15, 2012

### DonAntonio

"In most cases"? Division by zero is not defined. Period. Certainly some people use to write things like
$$\lim_{n\to\infty}\frac{1}{n}=\frac{1}{\infty}=0$$
but this is either a huge mistake (if the writer isn't aware of what he's doing) or else just an agreed shortwriting.

DonAntonio

8. Aug 23, 2012

### jtart2

Why doesn't someone just define it!!! ;)

9. Aug 23, 2012

### Mute

Because your definition has to be consistent with your other definitions, and there's no definition you can pick to make it consistent, at least in the usual number systems we work with.

10. Aug 23, 2012

### Studiot

Before you can define division by zero you have to define division.

Can you do this?

However the question of why is the subject not properly treated in maths classes when they reach a level to appreciate the answer is moot.

11. Aug 23, 2012

### dipole

In math it's not defined, but in physics division by zero is infinity. And it's not that physicists don't know what they're talking about, it's just that limits make for incredibly useful approximations, which you need to apply in order to get things done within the human lifespan.

12. Aug 23, 2012

### Number Nine

This isn't really an issue of limits.The limit of 1/x as x tends towards zero is not the same thing as 1/0. It is a fundamental property of the reals that zero does not have a multiplicative inverse; you can't add one without altering the behaviour of the entire system.

13. Aug 23, 2012

### dipole

That's not really my point, my point was that using the approximation 1/0 = ∞ leads to observable predictions which agree with experiment, so even if mathematically it is incorrect, in physics and other sciences it's enormously useful to define 1/0 to be infinity.

(And one can argue about what's more important, mathematical soundness or physical observation, but at the end of the day planes still fly and bridges don't fall down).

14. Aug 23, 2012

### chiro

Physical things deal with quantities that are measureable: you can't measure infinity or make sense of it in a tangible/physical sense so in terms of observation or physical quantification of some kind (for things like science and engineering), it's not useful in that regard.

15. Aug 23, 2012

### DonAntonio

I myself studied some physics while at undergraduate school, and all my best friends were physicists: division by zero is not defined

as infinity in physics, and that's a fact that can be pretty easily checked in any decent physics textbook (in mechanics, optics or whatever).

Now, some physicists can write $\frac{1}{0}=\infty\,$ , just as they can write $\,\frac{dy}{dx}=dy\cdot\frac{1}{dx}\,$ or

absurdities like these: it still is wrong, both within mathematics and within physics, unless there exists an a priori

agreement on what some weird notation may mean, just as writing "s.t." means nothing to anyone not knowing this is usually

taken to means "such that" in mathematics (and perhaps in some other areas as well)

DonAntonio

16. Aug 23, 2012

### Hurkyl

Staff Emeritus
No: what is enormously useful is to understand the concept that "medium / tiny = huge".