is 0 divided by 0 undefined ????

Question

is 0 divided by 0 undefined

Answer 1

0/0 is a discontinuity.

It is not specifically defined in the axioms of normal arithmetics. but, you can modify any set of axioms according to your own need, as long as they remain consistent and do not self contradict. U can define 0/0 to be 0, or u can define it to be 1 or 2 or 3... but before u proceed ahead, u have to make sure, by defining it as 1, your axioms do not self contradict. say,

0/0=1

what is (0/0) x0?

if normal arithmetical rules apply... that (a/b)c=(ac)/b

(0/0)x0=1x0=0
(0x0)/0=0/0=1

by setting 0/0=1, it contradict one of the rules, (a/b)c=(ac)/b, hence, in light of the original axioms, u cannot have 0/0=1.

The point is... as long as other rules r not broken, u can add definitions to mathematical objects to create a new object. U can still define 0/0=1, and change the (a/b)c=(ac)/b rule. u then have to make sure by removing this, other contradictions don't arise. Or u can set a rule saying, (a/b)c=(ac)/b applies except when (0/0)x0. again, u gotta check for contradictions. u can adjust everything until finally u have a new mathematical object that is wholly consistent with 0/0=1. Then, with this object, 0/0 is defined. Now, however, this new object would not behave like the ordinary number field we r familiar with.

Answer 2

L'Hopital's rule does *not* tell you
what 0/0 is, because 0/0 is what is called an "indeterminate"
quantity, which is to say that its value depends on what the situation
is. To convince your friends of this, ask them the following question:

"Find the limit of (ax)/x as a approaches 0 by using L'Hopital's
rule."

They will get "a" (trust me!).

But if you just put x = 0 in this expression, you get 0/0. So,
according to L'Hopital, 0/0 is equal to a.

Did you notice that I didn't say what "a" was? That's because it
doesn't matter. You can pick a equal to anything you want. For
instance, you could pick a = 1. Then you would get

0/0 = 1

Or pick a = - 3.14159. Then:

0/0 = - 3.14159.

So as you can see, 0/0 can be anything you want it to be. On the other
hand, in a particular problem, 0/0 might turn out to be something very
precise (and that's where you really do need calculus to understand
it!).

I think your argument for why 0/0 is undefined is a really good one.

However, I have another way of understanding why 0/0 doesn't make
sense, and it goes like this.

One way of understanding the fraction a/b is to think of it as the
answer to the following question:

"If I had a dollars, and b friends, and I distributed those a dollars
equally amongst my b friends, then how much money would each of my
friends get?"

The answer is that they would each get a/b dollars.

You can see that this works for fractions like 6/3, or 5/10, and so
on.

But try it for 0/3. If you have 0 dollars, and 3 friends, and you
distribute those 0 dollars (you're feeling generous...) equally
amongst each of them, how much would each of your 3 friends get?
Clearly, they would each get 0 dollars!

Now try it for 3/0. If you have 3 dollars and 0 friends, and you....
but how can you distribute any amount of money amongst friends who
don't exist? So the question of what 3/0 means makes no sense!

Now here's the kicker: What if you have 0 dollars and 0 friends? If
you distribute those 0 dollars equally amongst your 0 friends, how
much does each of those (nonexistent) friends get? Do you see that
this question makes no sense either? In particular, if 0/0 = 1, then
that would mean that each of your nonexistent friends got 1 dollar!
How could that be? Where would that dollar have come from?

Answer 3

It is undefined. Just think about what would happen if it were defined. You could get a proof like this:

0 = 0
0 = 0(3)
dividing by zero:
1 = 3

Answer 4

The answer is 0

Answer 5

It is undefined.
Consider the graph of y = 1/x
See how the graph looks near zero.
If you're on the left of zero, then the graph goes to negative infinity.
If you're on the right side of zero, then the graph goes to positive infinity.

Answer 6

it's like cutting a non existant pie with a non existant knife. it's undefined because it's irrelevant as nothing can come out of it.

Answer 7

yes it is undefined

Answer 8

It is undefined

Answer 9

yes

Answer 10

are you some kind of brainiac? Just ask your teacher. Why go ask us these mumble jumble questions?