# dividing 0?

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http://estfuture.blogspot.com/2010/07/dividign-with-zero-theory-in-eenglish.html

im not a math genius or teacher or anything. I dont know if anything similar has ever been done or not.

But that's what i wrote down... i just simply got that idea in the evening/night when i couldn't sleep and so i wrote it down.

Any thoughts, or hints to same work or pointing out flaws in it welcome (besides the posts that are just going to respond that u cant divide 0 - guess ur still 100% sure that earth is flat too).

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You are making this too difficult. If I divided nothing between any number of people, how much would everyone get?

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http://estfuture.blogspot.com/2010/07/dividign-with-zero-theory-in-eenglish.html

im not a math genius or teacher or anything. I dont know if anything similar has ever been done or not.

But that's what i wrote down... i just simply got that idea in the evening/night when i couldn't sleep and so i wrote it down.

Any thoughts, or hints to same work or pointing out flaws in it welcome (besides the posts that are just going to respond that u cant divide 0 - guess ur still 100% sure that earth is flat too).

You can divide zero. The answer is just always zero. You just can't divide by zero.

0/2 = 0

2/0 = undefined

If you divide zero apples among 2 people, they each get zero apples, obviously.

Dividing 2 apples among zero people... isn't a meaningful proposition.

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http://you-win-the-internet.com/

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just what i though posts in the style of "there is no way the earth in round. IT is flat -until proven otherwise - but that must be wrong and fake too".

ur telling me that u cant divide nothing... did u even read it? Was i dividing nothing there?

Edited by lifestream

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The inability to divide by zero is part of the definition of division. It's not a matter of "discovering" a way to do it. It's already defined to be impossible.

It's like I were to say, "mughubble is a new word. I define it to mean 'the shape of the Earth,'" and then someone later said "new research suggests that the Earth actually isn't mughubble!"

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It is extremely easy to divide zero. The result is zero. Dividing by zero, on the other hand, can't be done. You can divide by the absolute value of zero if you like; that gives you infinity (which isn't really a number). But you can't divide zero by zero, absolute values or no (the result is undefined).

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Waiiit a minute. I re-read the blog post and it's doing this:

$\frac{0}{2} = \infty, \, -\infty$

That's not division by zero! The blog post is specifically false in claiming that mathematicians say the above operation is impossible -- it's quite possible:

$\frac{0}{2} = 0$

It would not "mean the end of the world or the end of everything" as the blog post claims. There's absolutely no problem with dividing 0. Nobody says it's impossible.

I think the blogger doesn't quite get what the division by zero problem is. He invents a new answer to a question that already has a valid answer: 0.

I'm also unsure of the final formulas:

x means divider, n the value of the answer.

Even:

0 : x = (x : 2)n & -(x : 2)n

Odd:

0 : x = n & -n

How do we determine the value of the answer? If I want to do [imath]\frac{0}{x}[/imath], what is n?

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You can define division as being the inverse of multiplication. Meaning that given three numbers, $(a\in R,b\neq0,c\in R)$

If

$\left(a\right) \left(b\right)=c$

then

$a=\frac{c}{b}$

If you let $c=0$ as in the case you are proving you get:

$a=\frac{0}{b}$

meaning that

$\left(a\right)\left(b\right)=0$

Since $b\neq0$, then $a=0$.

Therefore for all numbers a and b expect when b equals 0:

$\frac{0}{b}=0$.

So you can divide 0, but not by how you do it. Also as other people pointed out your proof is really full of errors.

Edited by DJBruce

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If we divide by a number infintessimally larger than zero, we get infinity(well, technically taking the right handed limit of a/x as x approaches 0); If we divide by a number infitessimally smaller than zero, we get negative infinity(technically taking the left handed limit of a/x as x approaches 0). What should we get for a/0? The function of a/x is obviously not continguous over a domain including 0.

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just what i though posts in the style of "there is no way the earth in round. IT is flat -until proven otherwise - but that must be wrong and fake too".

ur telling me that u cant divide nothing... did u even read it? Was i dividing nothing there?

Nobody said you can't divide nothing. What everyone is saying is you can't divide by nothing. You can divide 0 apples between five people $(\frac{0}{5})$; every person get's exactly 0 apples. Dividing five apples between zero people $(\frac{5}{0})$, now that's impossible. How many apples would each person get?

And yes, you were dividing nothing, but apparently thinking you were dividing by nothing all along.

It is extremely easy to divide zero. The result is zero. Dividing by zero, on the other hand, can't be done. You can divide by the absolute value of zero if you like; that gives you infinity (which isn't really a number). But you can't divide zero by zero, absolute values or no (the result is undefined).

Really? I've never heard of that before. Do you know of any resource where I could read up on this? I tried a quick Google search but that didn't turn anything up.

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Really? I've never heard of that [division by |0| being possible] before. Do you know of any resource where I could read up on this? I tried a quick Google search but that didn't turn anything up.

That's because it's wrong. What Mr. Skeptic probably had in mind is that $\lim_{x\to 0} \frac{a}{x}$ (with any a>0) does not exist (approaching 0 from the left gives $-\infty$, approaching from the right gives $+\infty$) while $\lim_{x\to 0} \frac{a}{|x|} = +\infty$ formally seems to exist (if you accept that positive infinity was a result). That is, however, not the same as the question whether $\frac{a}{|0|}$ does exist. Mathematically, neither does the existence of a limit when approaching some point P imply the existence of the function at this point P, nor does the existence of the function a point P imply that the limit exists or equals this value.

For me, the most sensible meaning of division is purely algebraic. Algebra is something that is not taught in schools (despite parts of school math being called "algebra", there). In algebra, you define multiplication as a mapping of a pair of elements (numbers) on a single element (new number, product). Division there is the multiplication of an element with what is called the "inverse element". There is an inverse element for every element except one element which is called "zero" (the existence of such an inverse would violate the standard axioms). Hence, the multiplication with the inverse of zero does not exist hence the division by zero does not exist. Calculus, in particularly dividing by something else than zero, then taking limits and claiming that one did divide by something similar to zero so the result must be similar, strictly speaking has nothing to do with the question about division by zero (though in practice one often also calls something zero when one actually means something very small).

That is just the slightly more elaborate version of what was said before: Division by zero does not exist by definition. I'd say that pretty much every contrary statement seen on forums comes from the poster not knowing algebra (which is nothing to be ashamed of - it really is told in university courses, only), not from strokes of ingenuity.

(Shouldn't we have some FAQ about this topic? Probably occurs even more often than 0.999999... = 1)

Edited by timo

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That makes a lot more sense. Thanks.

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For me, the most sensible meaning of division is purely algebraic.

I agree with this.

What we have here is a field, that is set with two operations "addition" and "multiplication" that satisfy the axioms of "subtraction" and "division" with the caveat that the additive identity, the zero element has no inverse.

One can also have rings with no or some invertible elements.Supernumbers spring to mind here, but other things do come up in algebraic geometry.

(Shouldn't we have some FAQ about this topic? Probably occurs even more often than 0.999999... = 1)

I second that proposal.

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You deleted my contribution? Is it not okay to have a different answer to one of your guessed answers?

I believe personally you can divide 0, because 0 isn't a single number, it is a duality. This is my opinion, feel free to disagree.

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It was split to this thread. Further discussion can continue there.

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You deleted my contribution? Is it not okay to have a different answer to one of your guessed answers?

I believe personally you can divide 0, because 0 isn't a single number, it is a duality. This is my opinion, feel free to disagree.

!

Moderator Note

I believe your posts have been split into a separate topic.

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It's good to relax your definition to check things better in mathematics,

So, what i think is as following ...

[imath]a > 0[/imath] and [imath]b > 0[/imath] and [imath]c = \frac{b}{a} > 0[/imath]

[imath]\frac{0}{a} = \frac{b - b}{a} = \frac{+b}{a} + \frac{-b}{a} = \frac{b}{a} - \frac{b}{a}[/imath]

[imath]\frac{0}{a} = c - c = 0[/imath]

I hope my induction is simple enought ...

Edited by khaled

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