[kpux]

This is Zeno's paradox. It's an ancient Greek riddle. It's easily solvable with infinite series.

Basically, you can add up an infinite number of positive real numbers and have it come out to a finite sum. For simplicity, let's say the distance A|B = 1. In this example, 1/2 + 1/4 + 1/8 + ... + 1/(2^n) + ... = 1. Even though you are traversing an infinite number of halves, the total distance is still finite. Just because you can express the number 1 as an infinite sum of smaller real numbers, doesn't mean that A|B somehow becomes an infinite distance.