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→∞, 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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n such that n+1=−∞. But, see Real Projective Plane
Because you are suggesting that there is a numberAlso, modular arithmetic are built on circular number systems
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