For more than a thousand years, philosophers and mathmaticians have tried to understand Zeno's paradoxes, a set of riddles that suggest that motion should be impossible or that it is an illusion.
The paradox implies you can never leave the room you are in. In order to reach the door, you must first travel half the distance there. You'll also need to continue to half the remaining distance, and half again, and so on. You won't reach the door in a finite number of jumps! Mathmatically one can represent this limit if an infinite sequence of actions as the sum of a series (1/2 + 1/4 + 1/8...)
One modern tendnacy is to attempt to resolve Zeno's paradox by insisting that the sum of the infinite sries 1/2 + 1/4 + 1/8 is equal to 1. If each step is done in held as much time, the actual time to complete the infinite series is no different than the real time required to leave the room.
However, this approach may NOT provide a satisfying solution because it does not explain how one is able to finish going through an infinite number of points, one after the other. Today, mathematicians make use of infinitesimals (unimaginary tiny quantities that are almost but not quite zero) to provide a microscopic analysis of the paradox. Couples with a branch of mathematics called nonstandard analysis and, in particular, internal set theory, we may have resolved the paradox, but debate continues. Some have also argued that if space and time are discrete, the total number of jumps in a going from one point to the other must be finite.
According to Zeno's most famous paradox, the rabbit can never overtake the tortoise once the tortoise is given a head start. In fact, the paradox seems to imply that neither can ever cross the finish line.
