Lets say I take the natural numbers from 1 to infinity and I wrap the positive real line into a circle. So I have a circle with an infinite circumference and the natural numbers are spaced 1 unit away from each other at the edge of the circle. Now I draw a line from each natural number to the center of the circle. Now is there a point from the center of the circle at a finite distance such that there are no gaps in a second test circle drawn at this finite distance. And then can I construct a circle with infinite circumference and have an uncountable number of points and each point is separated from the other by a positive finite distance. And then draw a line from each point to the center of my circle. will I have another circle inside this that has no gaps in it.