What is 0 divided by 0?

It can be anything.

Anything multiplied by zero is zero.
That's why we call it "undefined"

0/0 is undefined (or meaningless).

0/0 is what is called an indeterminate form.

What it is (as a limit) depends on the context

in which it arises. Usually some algebraic

manipulation is needed to remove the form.

(Other indeterminate forms include ∞ / ∞,

∞ - ∞, 1^∞, and ∞^0)

Whatever 0 is divided by 0.

This is actually a fascinating question and one that has been pondered -- dare I say infinitely? -- over the last few hundred years.

To even have a chance to answer this, you need to know the contexts of the two zero values.

For an example, let me change the zeros into variables, the top 0 being X and the bottom 0 being Y.

Now, lets say that X = 1/2^n and Y = 1/3^n and let n start at 1 and go until infinity.

When n is infinity, 1/2^infinity is going to be 0.
When n is infinity, 1/3^infinity is going to be 0 as well.

But what about before that?

When n is 1, X is 1/2 and Y is 1/3 so X/Y = 1/2 / 1/3 = 3/2 = 1.50
When n is 2, X is 1/4 and Y is 1/9 so X/Y = 1/4 / 1/9 = 9/4 = 2.25

Since Y is going to 0 FASTER than X is going to 0, the result of X/Y is getting larger, so the limit of X/Y (that is the value just before X and Y equal 0) is going to be close to infinity (1/0 ==> infinity, sort of).

However, if X and Y are reversed, then X will go towards 0 faster than Y, and X/Y will get smaller, until the limit of X/Y will be 0 (0/1 ==> 0).

If there is enough information about the values, a definitive value for 0/0 (either infinity or zero) can be postulated. But if the only information is the values themselves, then 0/0 is undefined or indeterminate as it could be 0, it could be infinity, or it could be some other value all together. (For example, if X = Y = 1/n, then the limit of X/Y is 1 even though when n = infinity, X and Y are both 0.)

Cheers!

infinity, not defined

undefined.

0