# Simple Proof That Division By Zero Is Impossible

1. Sep 26, 2012

### Poolala

x / y = z, so z * y = x
1 / 0 = x, so x * 0 = 1
But 0 does not equal 1, so x / 0 is unsolvable.
Oh, and I'm new to forums so if this shouldn't be here you can delete it.

2. Sep 27, 2012

### RamaWolf

Perhaps you want to look at:

$\underbrace{lim}_{i->0} \frac{Sin(x)}{x} = 1$

3. Sep 27, 2012

### Simon Bridge

You mean:
$$\lim_{x\rightarrow 0}\frac{\sin(x)}{x}=1$$

... mathematicians can set up numbers to do all kinds of things.

4. Sep 27, 2012

### Hurkyl

Staff Emeritus
This argument makes the assumption that, whenever x/y is defined, the equation y(x/y) = x holds. It also makes the assumption that x0 is always defined, and it is 0.

Both of these assumptions are, indeed, true for the real number system, and the complex number system. But other important number systems do not have these properties.

RamaWolf is talking about something different (although some people have trouble distinguishing the two).

5. Sep 27, 2012

### HallsofIvy

Yes, that's a perfectly valid proof that the number 0 (or the additive identity in any field with more than one member) does not have an inverse.

True but has nothing to do with the topic here.

6. Sep 28, 2012

### Poolala

Oh, and I've been thinking: does 0 / 0 = 1, or is it undefined?

7. Sep 29, 2012

### ramsey2879

In most number systems 0/0 is undefined. Only a few exotic number systems have defined it and that is outside my scope.