What's 0/0? (Filler)(Filler)(Filler)

2 answers:

6 0

Anything divided by zero will produce an undefined result, because it is physically impossible to divide anything by zero.
When we say we are dividing by an arbitrary constant, we are saying we are finding the inverse of the multiplication sign.

For instance, when we say: $10 \div 5 = 2$ , we are saying that $5 \cdot 2 = 10$ . We have assigned some value, where the numbers have meaning.
So, in theory, we should be able to say that $0 \div 0 = C$ , where C is some arbitrary constant, right?

Well, no actually. We refer to the division sign as some sort of power, that when two things are simplified to form a fraction, then we can group them together.

Let's think about this process in grouping term:

Given 6 people, we can form 3 groups of 2:
A₁ A₂ B₁ B₂ C₁ C₂

This is what 6/2 forms; 3 groups of 2 people.
So, when we say 6/0 or 0/0, we can't physically and logically account for 0 people forming them into 0 groups, and mathematicians say that we have an indeterminate form, which makes the statement undefined.

The other way is the more intuitive way, and that is, to understand how limits work. For a function, f(x), we say that it has a limit, or a value where the function converges to. But 0/0 has no 'defined' mathematical value so we can't place a limit to it. Thus, it converges to infinity, and that's when we say it is indeterminate or undefined.