Why isn't there a quotient?

Question

Why isn't there a quotient for:
0/0
1/0
Please explain as fully as possible?

Answer 1

If you divide by zero the answer is undefined.
Imagine dividing 1 by 0.00001. The answer is big.
Now divide by 0.0000000000001. The answer is bigger.
As the number we divide by gets smaller, the answer gets bigger. The closer we get to dividing by zero, the bigger is the answer.

Now divide 1 by -0.00001. The answer is big and negative.
Now imagine diving 1 by -0.00000000001. The answer is bigger and negative.
As we divide by a smaller negative number the answer is a larger and larger negative number.
The closer we get to dividing by zero, the larger the negative number we get.

So, if we divide by a smaller number approaching zero from the positive side, we get a larger positive number. If we divide by a smaller number approaching zero from the negative side, we get a larger negative number.

If we could divide by zero, we would simultaneously have a very large positive number and a very large negative number which is impossible.

This is why we say that dividing by zero is undefined.

Answer 2

Your question is not entirely good already....

The problem is that that dividing by 0 does not make much sense; at least at a certain level of mathematical training.

1) Say you want to assign some number to the wanna-be quotient 1/0. Say you want 1/0 = x, where x is some number, we do not know which yet. What number would this be? If you want a coherent definition, which does not break the "rules" of mathematics; it makes sense to consider this: Since all other fractions of the form a/b=x imply that a=b*x; we would need to have, if we want to be consistent in our definition and avoid "definition by exception", it must be true that 1 = 0*x = 0. But this can never be true for some ordinary real number x. Simply put, zero times ANYTHING is again a zero. So there seems to be a glitch here.

2) The problem with 0/0 is even worse. The thought experiment we did above simply does not lead to a dead end. This is because 0 = 0*x for every x. So the problem now is not that the equation is not satisfied, but that it is satisfied for every possible choice of x. Which x do you pick as a definition of 0/0? Even if you pick something, what meaning will it have? All ordinary fractions have a meaning, something either geometrical or otherwise related to real life. And, if you allow for a definition of 0/0; why not 1/0?

3) Simply put, there are many problems with dividing by zero. I have not exhausted all. There are problems of MEANING [what will the fraction represent in real life?], and of COHERENCE [if we define it somehow, it will defy some other rules that would otherwise hold with only this one exception - mathematicians donot like that]. I am sure there are other problems too.

Answer 3

It's because division by zero is undefined.

Defining division by 0 complicates things.

Note that multiplication is the backwards process of division;
6 times 3 = 18, so 18 divided by 3 = 6.

9 divided by 3 is 3, and 3 times 3 is 9.

1 divided by 0 = ?, and ? times 0 = 1
What could possibly fit in the question mark? Also, what times 0 is equal to something non-zero? This is one of the things that makes this not work.

Answer 4

0/0-Anything divided into zero is zero. There is no way to divide zero into any number of parts and get an answer that is greater than zero.1/0 - You cannot divide any amount of anything into no parts. This is undefined.

Answer 5

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