Question

I have a theory, please tell me how far I am in the limits of Mathematics.
I propose that positive infinity and negative infinity are the same point (or space). My point is that when we take 0/0 we get infinity, and since zero is sign less so should infinity be.
Furthermore I say that the number line is circular and if I start moving towards infinity from the positive side, and if reach infinity and cross it, i will start coming back to zero from the negative side on the number line.
My reason for this statement is the graph of y=1/x.

Answer 1

As we approach close to zero for value of x (in positive) we move towards infinity. But after crossing x=0, when we get x=-value we start coming down from infinity on the other side.
Please Express your thoughts

Answer 2

Even though the logic is sound in one perspective, i dont think this is actually provable by other ways of looking at it, because then we should have derivatives on a number line too, and it should be presentable with an algebraic equation as such. . I'm not sure, but thats what i think :P
I have no idea what i have just said but the derivatives thing might give you a clue.

Answer 3

Certainly you can extend the number line to include \(\infty\), but when you do so, you must also include \(-\infty\) as well.

That being said, there is something called the Riemann Sphere which is kind of similar to what you're saying. Except instead of the number line, the Riemann Sphere is an extension of the complex numbers, and only adds \(+\infty\). http://en.wikipedia.org/wiki/Riemann_sphere

Answer 4

However, \(\frac{0}{0}\) is always undefined. It is neither \(0\), nor \(\pm\infty\).

Answer 5

THE ONLY WEAKNESS IN THE ARGUMENT IS the backbone of it- THE USE OF\[\frac{ 0 }{ 0 }\]

IT IS \[undefined\]
There is no way you can divide by zero ha ha ha. Say you have no bananas, and then you want to give them to "some children" which you do not have does that even make \[sense?\]

Answer 6

Even ideas that are wrong can lead to important and useful discoveries that are not wrong.

Answer 7

Yes, that is why there are experiments. Ideas coming from "wonder". All theories were derived from ideas as mentioned. However,trying to re-invent the wheel can never have any other outcome. Add-ons, yes, but a new round shape, never! Division by zero shall always be undefined. Many tried to prove otherwise. Try to answer this question, HOW MANY BANANAS WILL EACH PERSON RECEIVE IF TEN BANANAS ARE GIVE TO zero people? That is the humor in the whole idea!

Answer 8

Division by 0 is perfectly well-defined and well-behaved in the Riemann Sphere and the Extended Real Number Line provided that the numerator is not 0 as well. So yes, \(0/0\) is still undefined, and will likely remain that way except in some rather strange abstract structures, but division by 0 in other cases can easily be made to work.

Answer 9

Be that as it may, and as much as the root of a negative number can be found, we all know for sure that those special circumstances [ such as the Riemann Sphere] , shall always be mentioned as special, because mathematically, and scientifically, they are not of much gain, as they cannot be applied. So much so that it is prudent for a theorist to base a theory on something feasible,that can be proven. I mean, some can even prove that 0=1, yet, we know that in real life, and for the sake of developmental sciences, it will just be a special circumstance! But, yes, you are right, it is the mind that thinks out of the box, that brings new tidings.

Answer 10

Both of the examples I mentioned above have important real world applications. For example, without the extended real numbers we would be unable to say that the limit of a function is \(\pm\infty\). Also it's very important in Measure Theory, which is an area that makes integration/differentiation easier to work with.

As for the Riemann Sphere, I'm less familiar with it, but it's useful since you can use it to make holomorphic extensions of functions (very important in complex analysis), and it apparently is useful in particle physics and string theory.

But I will grant you that most structures where division by 0 is possible have much less use than these two examples. These two are special in their usefulness.

Answer 11

I will rest my case for now @KingGeorge , and go and dig more. For all we know, we might be both right.....or wrong! And thanx for the insight on the Measure Theory.

Answer 12

It was certainly a fun and interesting discussion we had. Hope to see you around!

Answer 13

Thanks a lot both of you.... i will study all the theories mentioned above...
Thanks..

Answer 14

always a pleasure, and no matter what u do, DON'T BE CONVINCED, UNTIL U R CONVINCED!