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Ok i found it really interesting and want to share my thoughts.

What i was thinking that what if a circle is a better way to represent numbers, I mean instead of number line there must be number circle. I mean there must be -infinity coinciding +infinity or there must be another no. just like 0 , I mean something maybe, maybe not.

Note by Shaswat Tripathi
1 year, 2 months ago

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Relevant article. · 1 year, 2 months ago

I knew these all and so it led me to my thought ^_^ · 1 year, 2 months ago

I've thought about this before, too. I don't think that representing numbers on a circle is exactly the same as the infinitely spanning line. You can approach a very, VERY large circle, but the fact that the circle closes in on itself I think makes it by its own definition to be finite.

I think this video is exactly what you're looking for to refine your thoughts; it will give you a nice visual representation of your circular number line idea. These are mechanical computers that were used in World War 2 for projectile accuracy, but it's like a function inside of a wheel.

Quantum bits are actually defined on a unit circle. · 1 year, 2 months ago

Is this about compactification? · 1 year, 2 months ago

This is about cams, which are a part of mechanical analogue computers. Think of it like a function along a wheel: as you turn the wheel (which represents the x value), you can see how much the y value changes along a follower that slides along a ruler.

· 1 year, 2 months ago

a small circle is enough to represent the no.s ,just like the line going infinitly long , I think the point where circle ends is the point where -infinity and +infinity coincides :D · 1 year, 2 months ago

Let's say you have a number line that goes all the way from $$x = -n$$ to $$x = n$$. Plot a function over this line. Then bend the number line into a circle.

If you plot for $$y = 2x$$, what does this look like when $$n = 10$$?

Which value do you get for this circle function when you want to look at the value for $$x = 10$$? What about $$x = -10$$?

If you take the limit as $$n \to \infty$$, what does this circle function look like?

(note: if we want to keep the function above the circle, we can add the minimum value of $$y$$ when $$x$$ is between $$-n$$ and $$n$$ to the function before we bend the number line) · 1 year, 2 months ago

why not keep it simple like let a circle be like 1,2,3......999999999999999999999999999999999999999999999.....till infinity and then a undefined no. be like next to it and after it negitive infinity,negetive infinty +1 and so ? i mean why it can't be true ? :D · 1 year, 2 months ago

Because you are suggesting that there is a number $$n$$ such that $$n+1 = -\infty$$. But, see Real Projective Plane

Also, modular arithmetic are built on circular number systems · 1 year, 2 months ago

ok what about a loop !is that good way to represent ? but hey i think what about assuming no -infinity exist like in the link you gave ? like 1,2,3................n and -1,-2,-3.............n ^_^ · 1 year, 2 months ago

There is no definite good way to represent what you're describing. All you need to establish this number system is a consistent set of axioms defining the behaviour of their members. · 1 year, 2 months ago

MAYBE YOU'R RIGHT,BUT STILL I THOUGHT :D · 1 year, 2 months ago

I did not claim that you're wrong. I just said that you need to jot down your ideas more formally · 1 year, 2 months ago