YES, I am up for a debate!

~Gata.

Let's see some equations first.

Sure, but first, I must say this.

CHUCK NORRIS HAS COUNTED TO NEGATIVE INFINITY

Negative infinity=/=infinity, because -1=/=1

Q.E.D.

Negative infinity = infinity * -1

Or = infinity - 2 * infinity

Negative infinity=/=infinity, because -1=/=1

Q.E.D.

Quod erat demonstrandum? Is that sarcastic?

Negative infinity = infinity * -1

 

Or = infinity - 2 * infinity

 

You mean:

"-∞" = "∞" * (-1) = "∞" -2 * "∞".

But you cannot calculate with ∞ like with any other number.

Negative infinity=/=infinity, because -1=/=1

Q.E.D.

Quod erat demonstrandum? Is that sarcastic?

Why should it?

Until you show us your proof, Sumiki, I will stick with Titan Alex Humva´s point.

~Gata.

I made a proof a while ago that proved this. Only it involved using the number that was bigger than infinity (biggest number), if infinity is taken to be an incredibly big number. So infinity isn't equal to negative infinity, but the number bigger than infinity is equal to the number smaller than negative infinity, just as 0 is equal to -0.

1/∞= 0.00000000000000.......00000001 (δ)

1/-∞=-0.00000000000000.......00000001 (-δ)

1/biggest number=0

1/-biggest number =0

0=-0

biggest number=-biggest number

This doesn't have many practical applications though. It creates two number scales based at 0 and the biggest number, which are separated by ∞.

This doesn't have many practical applications though.

I believe I have found the root of the issue here. =P

Infinity is not a number, it exists because people needed a word to call the never-ending list of numbers. Therefore, there can be no such thing as negative infinity.

Mildly relevant fact: 1 Potato is actually a number.

There are no real equations to this. It's a complex idea best shown on a graphing calculator, a quirky notion to explain a graphical oddity.

"Negative infinity" as I like to call it, is the infinite number of negative numbers there are.

Let's take a look at the graphs in question that made me come to this rather strange conclusion (after all, I did come up with this idea three years ago [yes, I was 11] and still have not found a way to disprove it):

The most reasonable one to see is one that goes straight to the point is the graph of one divided by X.

Fairly innocent, right?

Not so. To my keenly trained mathematical eye, I figured that it really wouldn't be so logical to have TWO separate lines. Logically, one equation, one line, right?

Seeing my calculator actually compute this, drawing a line that goes down into infinity and re-emerging at infinity on the other side. There's no way to get to infinity, though, that's the issue. It would go on forever, but it'd have to come out on the other side.

"But Sumiki!" I hear you cry. "Why don't the lines go all over the place?"

As it goes into positive infinity on the x axis, it would logically re-emerge, as per the theory, right on the line that the graph began with. So the graph is, essentially, repeating itself over and over and over again an infinite number of times. It will never deviate.

If one is willing to expand the concept a bit, let's take another common graph: X.

While it's a slightly smaller diagram, one can still see the same general idea: if it's one line, it will repeat itself as it travels to infinity and begins at negative infinity.

Hyperbolas illustrate the same point.

If you follow the line (easy to see on a graphing calculator), it can, once again, easily repeat itself - something that's two lines becomes the more logical one line.

Any questions now?

To my keenly trained mathematical eye, I figured that it really wouldn't be so logical to have TWO separate lines. Logically, one equation, one line, right?

Um . . . no. Functions can always have discontinuities. One function, one equation does not equal one line. Look at tangent graphs, which have infinite discontinuities.

Really, there seem to be a lot of holes in this theory. It's like you trying to say -1 equals 1, like Alex Humva said. That's something that obviously isn't the case.

~B~

Well, that's assuming something that infinity is a number - it's not.

Ah well. The whole point of this is to prove me wrong because it doesn't seem all that right.

First of all, infinity is a concept, not a number. It is the idea of numbers going on without ever ending. (Source: my maths teacher from last year, who had a Ph. D, so I'll assume she's very credible.)

Meanwhile, negative infinity is basically the idea of numbers going LOWER infinitely. It's used a lot as shorthand in notation of the domain or range of an equation, stating that the domain or range continues to become lower without end.

Finally, that first graph you used as "proof" is essentially just x^3=y when x=/=0, or something like that. My maths class is starting on this sort of thing in just a couple of months, so Ballom is probably the best source here.

~ BioGaia

Well, that's assuming something that infinity is a number - it's not.

Infinity is a concept, but then again so are all numbers if you want to look at it that way. I don't see the difference in -∞ ≠ ∞ compared to -1 ≠ 1, as both deal with concepts.

~B~

To my keenly trained mathematical eye, I figured that it really wouldn't be so logical to have TWO separate lines. Logically, one equation, one line, right?

 

Um . . . no. Functions can always have discontinuities. One function, one equation does not equal one line. Look at tangent graphs, which have infinite discontinuities.

 

Really, there seem to be a lot of holes in this theory. It's like you trying to say -1 equals 1, like Alex Humva said. That's something that obviously isn't the case.

 

~B~

The tangent graph continues up to infinity, then continues up from negative infinity. What Sumiki said also applies to this function, making it continuous.

There must be a number bigger than infinity, right? In terms of describing quantity, that number would be "everything". You can't have more than everything, because there is nothing more to have, just like you can't have less than zero (negative would be "owing" a number bigger than zero) because there is nothing less to have. Likewise there would be a number less than negative infinity, which would be "negative everything". If you continue decreasing a number past zero, the number will start increasing as a negative, and if you continue increasing a number past "everything", the number will start decreasing as a negative.

"Everything" is the opposite to zero (nothing), and it would have similar properties as zero, such as being the same as its negative. When you divide 3 by 0, you're finding out how many 0s fit in 3, to which the answer is more than infinity, it's "everything" rather than Maths Error. 3/-0 would be "negative everything", and because 0=-0, "everything" must equal "negative everything".

If you accept "everything" to be a number, then discontinuous graphs that increase to infinity then increase from negative infinity make sense as a continuous function. In a function y=f(x), y reaches "everything" after increasing past infinity, and then continues increasing from negative infinity, without every becoming discontinuous.

You can look at the continuation of x as well, such as in Sumiki's straight line graph. Eventually x will reach infinity, and pass it to reach "everything" far to the right of the graph image. After x passes "everything", it will be at the far left of the graph, at other end of the drawn function. This really completes the meaning of a "continuous function" for a straight line where no limits are specified, because it is a loop with no ends, rather than line with two discontinuous ends. There are no limits, where the function isn't continuous, no matter how big or small you get.

It would help if graphs were plotted on a cylinder with 0 on once side and "everything" on the opposite, or plotted on a sphere for both the x and y axis. But with today's technology, that's not possible, so we must settle for discontinuous lines and the rejection of zero's opposite.

"Everything" is the opposite to zero (nothing), and it would have similar properties as zero, such as being the same as its negative. When you divide 3 by 0, you're finding out how many 0s fit in 3, to which the answer is more than infinity, it's "everything" rather than Maths Error. 3/-0 would be "negative everything", and because 0=-0, "everything" must equal "negative everything".

The only problem with that is that dividing by zero isn't a legal math operation. However, even if it was, 3 divided by 0 wouldn't have an answer, not even "everything."

6/3 = 2 --> 6 = 2 x 3

3/0 = ? --> 3 = ? x 0

"Everything" is the opposite to zero (nothing), and it would have similar properties as zero, such as being the same as its negative. When you divide 3 by 0, you're finding out how many 0s fit in 3, to which the answer is more than infinity, it's "everything" rather than Maths Error. 3/-0 would be "negative everything", and because 0=-0, "everything" must equal "negative everything".

The only problem with that is that dividing by zero isn't a legal math operation. However, even if it was, 3 divided by 0 wouldn't have an answer, not even "everything."

 

6/3 = 2 --> 6 = 2 x 3

 

3/0 = ? --> 3 = ? x 0

 

Dividing by everything isn't a legal math operation either: 3/everything = ? --> 3= ? x everything. I wouldn't see it as illegal, rather they're both operations that lose information if you solve them, so they're best left unsolved.

There are no real equations to this. It's a complex idea best shown on a graphing calculator, a quirky notion to explain a graphical oddity.

 

"Negative infinity" as I like to call it, is the infinite number of negative numbers there are.

 

Let's take a look at the graphs in question that made me come to this rather strange conclusion (after all, I did come up with this idea three years ago [yes, I was 11] and still have not found a way to disprove it):

 

The most reasonable one to see is one that goes straight to the point is the graph of one divided by X.

 

 

Fairly innocent, right?

 

Not so. To my keenly trained mathematical eye, I figured that it really wouldn't be so logical to have TWO separate lines. Logically, one equation, one line, right?

 

Seeing my calculator actually compute this, drawing a line that goes down into infinity and re-emerging at infinity on the other side. There's no way to get to infinity, though, that's the issue. It would go on forever, but it'd have to come out on the other side.

 

"But Sumiki!" I hear you cry. "Why don't the lines go all over the place?"

 

As it goes into positive infinity on the x axis, it would logically re-emerge, as per the theory, right on the line that the graph began with. So the graph is, essentially, repeating itself over and over and over again an infinite number of times. It will never deviate.

 

If one is willing to expand the concept a bit, let's take another common graph: X.

 

 

While it's a slightly smaller diagram, one can still see the same general idea: if it's one line, it will repeat itself as it travels to infinity and begins at negative infinity.

 

Hyperbolas illustrate the same point.

 

 

If you follow the line (easy to see on a graphing calculator), it can, once again, easily repeat itself - something that's two lines becomes the more logical one line.

 

Any questions now?

Interestingly enough, Non-Euclidian Geometry--specifically Riemannian--works exactly this way, but with any given point on a graph. For anyone who doesn't know, Euclidian geometry--what most basic high school kids learn--is in 2D, where every point exists at one location on a plane. Riemannian geometry is 3D and can be applied to our reality. A line on a Riemannian plane goes around the whole three-dimensional surface (think sphere), so a point is in two locations--one location, and that location's exact geographical opposite on the other side of the geometric figure. Einstein's Theory of Relativity's based on this.

Anyway, my point is that this is a lot like Riemannian geometry, where a point basically is somewhere and then emerges on the other side.

Also, I still miss your proof. You seem to be saying it's legitimate to count 1, 2, 3, 4, -10, -9, -8, and so on until it repeats. Don't see the support.

There are no real equations to this. It's a complex idea best shown on a graphing calculator, a quirky notion to explain a graphical oddity.

 

"Negative infinity" as I like to call it, is the infinite number of negative numbers there are.

 

Let's take a look at the graphs in question that made me come to this rather strange conclusion (after all, I did come up with this idea three years ago [yes, I was 11] and still have not found a way to disprove it):

 

The most reasonable one to see is one that goes straight to the point is the graph of one divided by X.

 

 

Fairly innocent, right?

 

Not so. To my keenly trained mathematical eye, I figured that it really wouldn't be so logical to have TWO separate lines. Logically, one equation, one line, right?

 

Seeing my calculator actually compute this, drawing a line that goes down into infinity and re-emerging at infinity on the other side. There's no way to get to infinity, though, that's the issue. It would go on forever, but it'd have to come out on the other side.

Um, if your calculator churned that out, doesn't that mean your 'negative infinity' has already been discovered?

...Not to rain on your parade or anything...