What if there was an opposite of 0?

Question

It's been commonly told that the opposite of 0 is infinity, but what if there was a point that in a number line that was the imaginary junction between infinity and negative infinity on the number line. This would create a number circle of infinite length and turn a classic X,Y 2-D graph into a stretched out sphere.

Anyone ever think of this. Is there any interesting application of this concept?

Answer 1

There is an opposite of zero....in the binary number system. 0 normally represents "off", "low", or "negative" and 1 is it's complement as "on", "high" or "positive".

Answer 2

Have you ever studied projective geometry? It contains something similar to what you describe. Here is a very unmathematical desciption of what is done to construct the "real projective plane":
Begin with the Euclidean plane. To each family of parallel lines add an "ideal" point where they all intersect. Then collect all ideal points into an ideal line. Now it turns out that there is no way to distinguish the ideal points from any other points, and no way to distinguish the ideal line from the other lines. It is like giving the Euclidean plane a horizontal half-twist and joining the left "edge" at negative infinity to the right "edge" at infinity while simultaneously giving the plane a vertical half-twist and joining the top and bottom "edges" - the "cross-cap" from topology. (I told you this was a nonmathematical description!)
Among the results that follow are that there is now only one type of conic - the branches of parabolas and hyperbolas "join at infinity" to form closed curves just like the ellipse.
Don't show my description to any real mathematicians, but do check out the real projective plane.

Answer 3

It could be argued that any number is the opposite of zero. Mathematics is just another language to explain things and describe things. Zero was invented as part of mathematics not to be the mathematical equivalent of "nothing," but was invented by Arab mathematicians who were studying Greek Geometry. They found that if they wanted to find unkown values (algebra) they needed an integer to serve as a place holder to demark 10's from 20's from 30's etc. The zero shows that the mathematician is showng the value of thirty, not three, or minus thirty, not minus three. Think of it this way, and this is what the early mathemeticans said about their new science - "the map is not the territory." Zero just makes the map easier to draw.

Answer 4

Hmmmm....Interesting.

I think it's hard to have an absolute opposite of a singularity (zero). Especially when imaginary & infinites are concerned.

Good argument here is a timeline. We live & observe a linear timeline. Every cause has one and only one effect.

What about planar time? One cause could have two effects but you know both effects.

Cubic time? One cause has two effects, you know both effects, but also another effect to cause both the same effects?

Singularities are non-negotiable.

Answer 5

no application . if you ever think of such sums then the entire maths is wrong.
there would be MOD 0
TRIGNOMETRY AND CALCULUS WOULD TURN MEANINGLESS.

EVERY SUM INVOLVING 0 WOULD HAVE A DEFINITE CHANGE IN ANSWER AS SOME WOULD CONSIDER 0 AS EVEN DIGIT ,OTHERS AS ODD BUT NOT NUETRAL.
EVEN ADDITION AND SUBTRCTION WOULD HAVE DIFFICULTIES.
DONOT EVEN IMAGINE THINGS LIKE THAT

Answer 6

Dude you need one of my custom reefers to puzzle your self a little less.