# Simple Proof That Division By Zero Is Impossible

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.

RamaWolf
Perhaps you want to look at:

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

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

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

Staff Emeritus
Gold Member
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.

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).

Homework Helper
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.
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.

Perhaps you want to look at:

$\underbrace{lim}_{i->0} \frac{Sin(x)}{x} = 1$
True but has nothing to do with the topic here.

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

ramsey2879
Oh, and I've been thinking: does 0 / 0 = 1, or is it undefined?
In most number systems 0/0 is undefined. Only a few exotic number systems have defined it and that is outside my scope.