Does The Pattern Continue?

The answer lies within the properties of relations and functions.

Let us assume a function that says:

$f(x) = \frac{0}{0}$

Since it is constant divided by a constant, any value of x satisfies this function.

Also $\frac{0}{0}=c \Rightarrow 0c=0$

Therefore, value of f(x) can be any value.

Now, by properties of relations and function one or many value of x can yield one value of f(x). Also know as one-one and onto functions. But, one value of x can never yield many values of f(x).

So by contradiction $f(x)\ is \ not \ a\ function$ ,

and hence, value of f(x) value cannot be determined.

Imagine that you have zero cookies and you split them evenly among zero friends. How many cookies does each person get? See? It doesn't make sense. And Cookie Monster is sad that there are no cookies, and you are sad that you have no friends.

Let $\displaystyle \frac{0}{0}=x$ :

$\frac{0}{0}=x \Rightarrow 0x=0$

$\displaystyle x$ fits with all real numbers ( $x \in \mathbb{R}$ ).Therefore, the answer is Inderterminate.

Everything divides 0 is 0

As a general rule, anything with ∞ and many things with a 0 are problematic.

0/0, 0^0, ∞/∞, 0 * ∞, ∞ - ∞, ∞^0, and 1^∞ are all indeterminate/undefined

zero can never be a factor ...... so thats indeterminate.

Any number divided by 0 = not defined