# Dividing by zero explained?

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x/0=undefined; x>0

Undefined= indefinite form or value.

Because zero is zero or the absence of value (and all this other number theory crap), it can go into any non zero number as many times as it can, but because of the fact that it "can" go into a non-zero number any amount of times, however many times it actually goes into something is undefined or cannot be kept track of.

Opinion: If something doesn't define how many times 0 goes into a non-zero number, it simply does it infinite or at least indefinite times, which explains why mass in 0 volume = infinite density, because math wise it would be x/0; x>0. And then, what if you do in fact define it? Say I have a value of 0 and I want to put it into another value because putting the value of 0 into another number will do something (like I program "when divide by x, do this; x=0", since 0 doesn't use up any material, I can do it however many times I want without using up anything, but in that instance, don't I define how many times it goes into 0 and therefore give an answer to the problem x/0, like if I want to do it 10 times, wouldn't x/0=10? There's also that unit circle thing where at 90 degrees, tan=infinity or undefined, but what's occurring is 1/0, so couldn't I say the cause of infinity is 1/0 because literally any length "can" satisfy that scenario and make a triangle as long as it's greater than 1?

More like speculation:

Dividing 0/0

0/0=1?

0^1/0^1=0^0=1?

Perhaps 0/0 does in fact equal 1, but we haven't found where it occurs in nature or where we can perceive it. Maybe there's some kind of quantum mechanical thing that it happens with where something of 0 size somehow has some kind of wave function and you divide nothingness by a boundary of 0 and get something that spreads out infinitely through space or something.

Exploring rule of dividing by 0:

In that unit circle thing I mentioned early, tanA=sinA/cosA, but at 90 degrees or where the sin=1 divided by cos=0, there are infinite possible side lengths of which you can make a triangle, BUT, if you use a length to make the other leg which is less than 1 at 90 degrees, even though the other leg is basically a point (or seems to be), it still needs to be a triangle, and the only way to have a triangle is with 3 sides, but the only side lengths that will satisfy making a triangle in that situation when sin=1 and cos=0 are any number above 1 but including 1, which leads me to think that the rule for dividing by 0 is

x/0=x+R

R=all real numbers,

I probably did the equation wrong, but what I was trying to say is that x/0 equals every number, x and above to infinity, not less than x. Although if you do -1 divided by 0, I don't know.

By the way, R includes 0 right?

Edited by questionposter
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since 0 doesn't use up any material, I can do it however many times I want without using up anything, but in that instance, don't I define how many times it goes into 0 [...]

I don't think that provides any definition. If I have some quantity, and I ask "How many times can I take away 0 before the quantity is all gone?", there is no answer. It's not any finite number, and it's not infinite either (infinity times 0 is still 0... you could take away nothing forever and the original quantity will remain unchanged).

If you plot 1/x, it approaches -infinity as -x approaches 0, and +infinity as +x approaches 0. I've always thought of "1/0 is undefined" as meaning that it could be any value from -infinity to +infinity... it has no definite value. But the above example suggests that it really means "no possible value".

Edit: Your example, now that I read the whole thing, sounds more like "How many times can I divide 0 into separate piles" or something, and that is more like 0/x, which is defined: it is 0. x is unknown or can be any non-zero value... but I don't think that makes it undefined. Your question is basically "solve for x" where "x has infinitely many solutions."

0/0=1?

I don't see how you could possibly figure that, given that x/0 is undefined.

However, I think it might be possible to try to argue that 0/0 = 0.

If you have x/0 is undefined in the sense that it could be any value and so isn't defined, but you multiply it by 0, the result will be 0 regardless of what x/0 might represent. In a sense, multiplying by 0 can restore definition???

But, given your example above, I'd say 0/0 or 0*x/0 is still undefined. x/0 does not mean "can be any number". I'd say it can better be described as "cannot be defined as a number." Multiplication is not defined for something that is not defined, so 0 * q is not 0 for all possible things q outside of the realm of numbers! Perhaps there is some operation that can be performed on undefined things and result in a number, but basic math operations ain't it. Anything divided by 0 is undefined and any math operation you perform on the result will also be undefined.

Ain't no mathmertician so I reckon someone else'll explain this better.

Edited by md65536
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infinity times 0 is still 0

Nope.

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Infinity times zero is zero because zero kills the equation, by law. Nothing, nada, kaput.

We're not talking about how one number affects another, like in addition or subtraction. We're talking about a product between a rational, yet undefined number and zero, which always produces zero.

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Infinity times zero is zero because zero kills the equation, by law. Nothing, nada, kaput.

We're not talking about how one number affects another, like in addition or subtraction. We're talking about a product between a rational, yet undefined number and zero, which always produces zero.

Infinity isn't the number though, it is the existence of counting without end and instantaneously reaching the "without end". It goes on forever.

I don't think that provides any definition. If I have some quantity, and I ask "How many times can I take away 0 before the quantity is all gone?", there is no answer. It's not any finite number, and it's not infinite either (infinity times 0 is still 0... you could take away nothing forever and the original quantity will remain unchanged).

But it's undefined because you can't define how many times it happens. It doesn't have a specific answer because there is nothing determining the answer because it can be literally any number, so since nothing is determining the answer, it's just undefined, not infinitely.

Edited by questionposter
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infinity times 0 is still 0

Nope.

It is defined as 0, in measure theory.

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Nope.

I seem to be mistaken. There is a good discussion about it here: http://www.physicsfo...ad.php?t=118941

I feel inclined to argue about limits... that 0 times infinity is indeterminate because it uses the "limit as x approaches zero" instead of 0 itself... but I think that is the point. In my example I'd used "infinity" as if it were a number, and that doesn't make sense. I should have said "an arbitrarily large number times 0 is still 0", or I may have gotten away with "an infinitely large number times 0 is still 0". The point is that an infinitely large number is a number (is that valid?) while 'infinity' is not.

So if we want to treat infinity as a number, we have to do so using limits.

That being the case, the question "How many times would I have to take away 0 from some quantity until it is all gone?", might validly be answered with "infinity", meaning "Not any finite number", meaning "No matter how many times you take away 0, it will not be enough to eliminate that quantity."

Your link suggests a clue to the discussion though. The word "indeterminate" seems to indicate a number that can be anything, but it's still a number. "Undefined" seems to indicate the same, but also includes the possibility that the result is not a number at all (or that it's impossible or doesn't make sense).

I'm in over my head, but I googled it and found this: http://mathforum.org....divideby0.html

'Why is 0/0 "indeterminate" and 1/0 "undefined"?'

So I was wrong, but there's some way forward with this. 0/0 appears not to be "undefined".

The solution to "0/x = 0" for x would be indeterminate.

It is the same reasoning that x could be anything in 0 = 0*x, while 1 = 0*x is not true for any number x.

Addendum: I was wrong; 0/0 = 1 is as valid as 0/0 = 0. However I still think that 0*(0/0) might still be 0! Multiplication by 0 doesn't make an undefined thing into 0, but it should make an indeterminate number into 0.

Asking "what is 0/0?" in terms of the example I've been using, is like asking "How many times can I take 0 away from 0 until it is gone?" An answer of "0" works, but so does an answer of "1". Or 10. Or any number. It is indeterminate.

Asking "What is 0*(0/0)?" is like asking "Given the task (of repeatedly taking away 0 from 0 some indeterminate number of times to end up with 0), if I repeated this 0 times, how many times would I have taken away a 0?" Not the best of wording... but the answer is 0.

Edited by md65536
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Nope.

nope.

That Wiki article applies to indeterminate forms of limits, which are irrelevant to the question.

Even in the theory of cardinal numbers 0 times any cardinal is still 0.

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nope.

That Wiki article applies to indeterminate forms of limits, which are irrelevant to the question.

Even in the theory of cardinal numbers 0 times any cardinal is still 0.

So I can literally say "never ending amount instantaneously which cannot be matched in counting speed 0 times is 0"? I guess that would make sense, but infinity itself isn't a number, so wouldn't multiplying by a number not work because the 0 can't eliminate all of the numbers since they keep counting forever and count at a greater speed than multiplying a number can effect them? How can you eliminate something that goes on forever? It's like saying I can reach the end of a never ending path, or that I can destroy the universe even though it has no boundaries (as far as we know). In most cases I don't think you actually count at the speed of infinity.

Edited by questionposter
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nope.

That Wiki article applies to indeterminate forms of limits, which are irrelevant to the question.

Even in the theory of cardinal numbers 0 times any cardinal is still 0.

True, though up until now I believed $0 \cdot \infty$ was indeterminate regardless of the context. Are you saying it's zero?

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But why do you have stuff like -∞< x < ∞ instead of -∞ = x = ∞ if you can actually count to/at the speed of infinity?

Edited by questionposter
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• 1 month later...

0 cannot interact with any form of number, therefore, is neutral. 0 is a necessary concept in order to make maths an entirely logical discipline.

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So I can literally say "never ending amount instantaneously which cannot be matched in counting speed 0 times is 0"? I guess that would make sense, but infinity itself isn't a number, so wouldn't multiplying by a number not work because the 0 can't eliminate all of the numbers since they keep counting forever and count at a greater speed than multiplying a number can effect them? How can you eliminate something that goes on forever? It's like saying I can reach the end of a never ending path, or that I can destroy the universe even though it has no boundaries (as far as we know). In most cases I don't think you actually count at the speed of infinity.

In the theory of cardinal numbers there are LOTS of infinite cardinals. They can be added and multiplied, but addition and multiplication do not follow the rules that you are used to seeing for integers.

While you can certainly utter the phrase "never ending amount instantaneously which cannot be matched in counting speed 0 times is 0", I doubt that anyone, including you, will understand it.

In the extended real numbers $0 \times \infty$ and $\frac {1}{0}$ are meaningless.

Edited by DrRocket
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In the theory of cardinal numbers there are LOTS of infinite cardinals. They can be added and multiplied, but addition and multiplication do not follow the rules that you are used to seeing for integers.

While you can certainly utter the phrase "never ending amount instantaneously which cannot be matched in counting speed 0 times is 0", I doubt that anyone, including you, will understand it.

In the extended real numbers $0 \times \infty$ and $\frac {1}{0}$ are meaningless.

Well I know infinity has it's own rules, and that just goes to show that it isn't an actual number, it's it's own thing, it's everything simultaneously.

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Well I know infinity has it's own rules, and that just goes to show that it isn't an actual number, it's it's own thing, it's everything simultaneously.

Wrong.

Go read what I said and also read up on cardinal numbers. Naive Set Theory by Halmos is a good source.

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