Little explorations with HP calculators (no Prime)

[Joe Horn]

(09-09-2017 09:21 PM)pier4r Wrote:  (a) assuming that they have unlimited capacity and they keep running forever, would they meet again in a place while running?

If Alan and Bob are mathematical points with no extension, then NO. Let's assume that the outer perimeter is 4. At all 4 midpoints, the distance covered by the outer runner will always be a rational number, and the distance covered by the inner runner will always be an irrational number, and hence never equal. The same logic applies regardless of the actual measurements.

If Alan and Bob are actual physical beings, then YES. If they never speed up, slow down, or veer off course, then bumping into each other is inevitable.

EDIT: The first paragraph is only true in an abstract, non-physical reality. In THIS universe, where everything seems to be made up of discrete quanta, I suppose even infinitely small points would eventually meet as they hop-scotch in contiguous, minuscule jumps (quantum leaps?), rather than moving smoothly and continuously, along their respective paths.