
#1
Jan2404, 01:55 AM

P: 235

Infinity and negative infinity are widely known to be equal. So, with that premise, I shall continue.
To extend the number line infinitely along the positive direction results in infinity. To extend it in the negative direction results in negative infinity. These two infinities are equal therefore the number line can be visualized as a circle rather than a line. At one pole is zero, at the other infinity. What differentiates infinity from zero then? What reason exists that prohibits its use as a base like zero? Here is a diagram: Diagram My idea is this: Infinity can be used as a base for a number stystem just as validly as zero can. In the diagram, addition is shown as clockwise, subtraction counterclockwise. No matter how much we add to zero, we never reach infinity. No matter how much we add to infinity, we never reach zero. The same goes for subtraction. Why is this? Technicly the point that is never reached is that point halfway between zero and infinity. Perhaps the distance between numbers actually grows smaller the larger the numbers one deals with the distance between 20,000 and 20,001 for instance would be smaller than the distance between 5 and 6. As a last idea (it's getting rather late), here are some "undefined" equations defined. I=infinity. Note that they are defined on the infinitybased number system, but still have no meaning to the zerobased system (those that's results have to do with infinity, that is). 0/0 = I I/I = 0 x/0 = Ix x/I = 0x 



#2
Jan2404, 02:48 AM

Emeritus
Sci Advisor
PF Gold
P: 16,101

What is correct is that one extension to the real numbers adds a single point at infinity that turns the real line into a "circle". By "circle" I mean something that has the topology of a circle; it is a mistake to think of this too literally as being a real circle embedded in a plane. However, there is one interesting thing about this particular extension of the real numbers: if we exclude 0, we can then define a new addition: [tex]a \oplus b = \frac{ab}{a+b}[/tex] and extend multiplication and addition to [itex]\infty[/itex] by [itex]\infty \oplus x = x[/itex] and [itex]\infty x = \infty[/itex] for all x. It turns out that this new structure is isomorphic to the ordinary real numbers; for instance, the distributive law holds: [itex]a (b \oplus c) = a b \oplus a c[/itex]. 



#3
Jan2704, 10:12 PM

P: 235

0/0 = II = I I/I = 00 = 0 x/0 = Ix x/I = 0x I0 = I 0I = 0 Really simple stuff, I havn't done anything complicated or revolutionary (or useful, most likely[6)]) simply added another "number system" counting "down" from infinity towards zero instead of the other way around and connected it with the zerobased system.[ 



#4
Jan2804, 06:19 AM

Sci Advisor
HW Helper
P: 9,398

Infinity/Negative Infinity and ZeroAs we are using the one point compactification, surely there are two numbers halfway between 0 and infinity? 



#5
Jan2804, 06:44 PM

P: 235





#6
Jun2204, 08:52 PM

P: 1

this link has something to do with what your talking about
http://www.writing.com/main/view_item/item_id/854403 


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