Remember the busy Bee
? The one that kept flying from the bicyclist to his home and back as he approached it?
Well, at the instant when the person finally got to his house, which way was the Bee facing? (Assume that the Bee's turns are instantaneous - that it can go from facing the house to facing the cyclist in no time.)
The bee would be making an infinite number of to and fro movements from the bicyclist and his home.
It would be impossible to determine the precise direction the bee would be facing, as doing so would be to imply that the bee is facing either the biker or the house, so that the number of turns taken by the bee is either even or odd, and therefore finite.
This would contradict the bee taking an infinite number of turns, and accordingly, we would arrive at a paradox.