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 A Former Brilliant Member
5 years, 1 month ago

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- 5 years, 1 month ago

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

- 5 years, 1 month 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.

- 5 years, 1 month ago

- 5 years, 1 month 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.

- 5 years, 1 month 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

- 5 years, 1 month 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)

- 5 years, 1 month 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

- 5 years, 1 month 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

- 5 years, 1 month 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 ^_^

- 5 years, 1 month 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.

- 5 years, 1 month ago

MAYBE YOU'R RIGHT,BUT STILL I THOUGHT :D

- 5 years, 1 month ago

I did not claim that you're wrong. I just said that you need to jot down your ideas more formally

- 5 years, 1 month ago

yeah thanks for your time anyway :)

- 5 years, 1 month ago

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