Awww isn't that cute, Bucky is pretending to be a girl of science. Its so adorable when children play act.<quoted text>
Distance is not an abstract extension. Distance is a quantity of measurement yielded by physical properties.
Your closed loop offered as an actual physical infinity either (a) must be rejected because it is imaginary, or (b) must conform to physical properties like distance.
If required to conform as in (b), then one revolution of the loop is an infinite distance because you are proposing an infinite total distance.
If the total of travel in the loop is infinite, as you propose, then any portion is infinite.
Where "i" is infinity, i/N = i.
Yours is the special pleading. You want your loop to be proof of a physical infinite, but not conform to physical properties.
Let me know when you get to high school and study physics, math, geometry and pre-calculus. Then we can have a grown up discussion about the universe and concepts like infinity