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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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
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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
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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 ^_^
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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.
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MAYBE YOU'R RIGHT,BUT STILL I THOUGHT :D
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I did not claim that you're wrong. I just said that you need to jot down your ideas more formally
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yeah thanks for your time anyway :)
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