Please refer to following link

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.

Thanks for reading this!

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I knew these all and so it led me to my thought ^_^

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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.

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Is this about compactification?

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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.

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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

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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)

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Real Projective Plane

Because you are suggesting that there is a number \(n\) such that \(n+1 = -\infty\). But, seeAlso, modular arithmetic are built on circular number systems

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