what is ZERO divided by ZERO?

Question

Can i say: since any number divided by itself is 1 then zero divided by zero the ans is 1?

Answer 1

Divide by 0
Error

Answer 2

First of all, no one said that any number divided by itself is 1. The rules say for example, that if a rational number e is multiplied by another number 1/e. where e is not zero*, results in 1, then 1/e is the reciprocal of e.

This can be rewritten to mean that any number e multiplied by its reciprocal 1/e, where e is not 0, will yield 1 as a result. The key here is the phrase "where e is not 0".

Instead of multiplying by 1/e, people choose to divide by e which is virtually the same. Following the laws however means that diving a rational number by itself yields 1 if the number being divided by is not 0.Not fully understanding the laws you are working with yields the kinds of questions that you have now.

0 divided by 0 is undefined by definition.

Answer 3

Zero divided by zero is "undefined" and that is the most that can be said about the quantity.

Here's the reason:
You're basically looking for the value of X in this equation:
0/0 = X
If you knew what X was, you would have the answer to your question. So, let us rewrite the equation in slightly different form:
0 = X*0
Notice I have simply multiplied both sides by zero. What value of X satisfies this equation? If X = 1, then we have
0 = 1*0
which is true. If X = 2, then we have
0 = 2*0
which is true. This works for any value of X, therefore X has no single answer. In other words, X is not well-defined by our initial equation. So, the most we can say about X is that it is undefined:
0/0 = undefined.

Answer 4

I am no math professor, but however unlocks this answer will find the keys to the universe waiting for them. The book answer is that it is either indeterminate which in my mind means that either nobody knows what the answer will be given a specific case.

Here is where I start scratching my head.

If 5x0=0 then by dividing both sides by 0 gives us 0=0/5. This is obviously true.

However, dividing both sides by 5 gives us 5=0/0 and this may be true and may not be true. You can replace 5 by any number and it will be equal to 0/0.

Someone much smarter than I is going to crack this code and it will be the biggest discovery since, well, the discovery of the number zero.

Answer 5

ZERO divided by ZERO is undefined because we con not say that if I have nothing and I want to divided to nothing the result well be one (How come)
This problem try to stay away from it because no one try and get answer from it
Plus for your information if you divide any number by zero you get the result is undefined but if you start to study limits course
this result well change into infinity

Answer 6

You can say that but you'd be wrong.

Zero divided by any number is zero.

Any number divided by zero is an error or impossible.

So if you can make your answer explain these 2 rules as well, then feel free to share with the rest of the world your discovery.

Answer 7

it depends...
if you take 0 / 0, and these values are EXACTLY ZERO, then the answer is undefined... why ? it is unclear how many times zero can be divided into any number , even into zero itself !!!

[ for ex... 3 / 0 = undef. , how many zeros are in 3 ?.....5?...28 ?....2 billion ?....???????, and for 0 / 0, it is the same... ]

if, on the other hand, 0 /0 represents two very small quantities that APPROACH zero as a limit [ as in Calculus ], then the answer is Temporarily indeterminate ... that is the answer is yet to be decided...

for example limit [ x^2 - 1 ] / ( x - 1 ), as x --> 1 would appear to give us
0 / 0, when 1 is plugged in, but in fact, the answer is 2

In Calculus, " 0 ", is not necessarily zero, but may represent a very small number, very very, close to zero.... { I know, the notation is confusing, but that's the way it's done }
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Answer 8

I think if you divide an equation by zero, then it renders it wrong.... in my math text book it proved 1=2 by dividing both sides by zero... don't really understand it either :)

Answer 9

Think about it this way...

there are 0 things to be divided among 0 people... how many does each person get?

there is no answer because there are A) no people B) nothing to divide...

Answer 10

No...0/0 is an indeterminant form. Anything divided by zero is infinity. But zero divided by anything is zero.

Answer 11

What you can do is take the limit as some value approaches 0 divided by the limit as some other value approaches 0.

For example:

The limit of x/x as x approaches 0 is one.
The limit of x/2x as x approaches 0 is 1/2.

So 0/0 is undefined because it could be anything or nothing.

This is why we have calculus. To figure out what these limits are.