Dividing Zero By Zero

But if zero can go into zero 1 time how can it go into zero 2 times? And three and four?

I am not quite understanding your question, but let me put it in a simpler way. Division is a series of subtractions: asking for the quotient of six divided by two is the same as asking how many times we can subtract two from six until we get zero, which is three times. And asking how many times we can subtract zero from zero until we get zero leads to the answers: one, two, three, and so on, that is, any number of times -- zero divided by zero is any number.

But just like any other number shouldn't zero divided by zero equal one not 2, 3, 4, etc....

does zero, have sustance of any sort or kind ?

not to me

Seek, and ye shall find.

nothing

How about dividing dividing ? what is it that you get ?

Any nonzero number divided by itself is just one, but although zero divided by zero is one as well, it is also any other number. That's why any other number divided by zero is called "undefined," while zero divided by zero is called "indeterminate." The word "undefined" means that no number -- including zero -- multiplied by zero results in a nonzero number, precisely because any number multiplied by zero results in zero, so the division of zero by zero results in any number, being thus called "indeterminate." If the division of zero by zero were well-defined, then it would be allowed in mathematics, which it is not. In mathematics, no division by zero is well-defined, or hence allowed: the division of a nonzero number by zero has no possible result, while the division of zero by zero has all possible results.

Zero is a number, so it has the same substance of any other number, which is the substance of an abstract entity.

If you don't seek, then you will certainly find nothing.

If you are lucky.

I get it now!

I am glad you do. So this is the mathematical situation: zero divided by zero is any number. The problem is that it makes any number identical to any other one, which makes all numbers false, because no number can be identical to a different number and still be a true number. On the other hand, numbers must be different from each other for the division of zero by zero to have all its possible quotients, one at a time. So numbers must be true to be false: they must be different from each other for the division of zero by zero to make them all the same. And numbers must be false to be true: the division of zero by zero with each possible quotient remains valid if numbers are true, so all numbers must be false to be true. This is analogous to the Liar paradox, given by the sentence "right now, I am lying," which must also be true to be false and false to be true.

And you've lost me again...

The quotient of zero divided by zero being any number is a mathematical fact and a practical reason for its not being allowed in mathematics. However, its making all numbers false, of which the prerequisite is all numbers being true, is my philosophical thinking. What you are not getting now is not simply mathematical anymore, it is my philosophy, so let me try to explain it to you.

If you accept dividing zero by zero, the consequence is that any number is identical to any other number. For example:

1) Zero equals zero:
0 = 0

2) Any number multiplied by zero equals zero:
1 × 0 = 2 × 0

3) Zero divided by zero equals one:
1 = 2

4) Zero divided by zero equals two:
2 = 4

Now, if any number is identical to any other number, then all numbers are false. Why? Simply because a true number must be different from any other number, according to the definition of a number by Bertrand Russell -- a number is a class of similar classes, two similar classes having a biunivocal relationship between their elements. If two different numbers are the same, then they are no longer two classes of similar classes, hence are false numbers.

However, the division of zero by zero as having any particular quotient requires that all numbers are true, since we wouldn't be able to even formulate it without numbers -- true ones. Hence, numbers must be true to be false -- via the division of zero by zero.

Conversely, since there is no mathematical reason for a division of zero by zero resulting in one to be considered less valid than any other division resulting in one, numbers must be false to be true. Although mathematicians would not allow the division of zero by zero so as to preserve mathematics from self-destruction, mathematics itself has nothing against it: it would self-destruct if left alone -- like computer programs do sometimes -- because numbers must be false to be true.

There is a sentence that behaves in exactly the same way -- it must be false to be true and it must be true to be false -- which is "right now, I am lying," known as the "Liar paradox."

Anyone who knows anything about mathematics - which excludes you - can see instantly why your argument is nonsensical; stop confusing the innocent with allegedly philosophical paradoxes! Hint: no mathematician can be found to agree with you, as you would know by consulting any standard text:

http://mathworld.wolfram.com/DivisionbyZero.html

He's lost you because he's hopelessly lost himself. Read the link I just posted and come back here with questions, if any.

I get it I get it.

Nono I understand again.

Why don't you go to that link and read it again? Here is what it says:



Besides the fact that a number that approaches zero must not be zero, the article is clear enough in saying that such a limit may be well-defined, which means it also may be not. However, since I am talking about the division of zero by zero, you example is useless, since it divides not zero, but one, and not by zero, but by a number that approaches zero. Additionally, the article says "undefined" because it is talking about the division of any number by zero. Were it specifically talking about the division of zero by zero it would say "indeterminate."