Achilles and Tortoise Paradox

Achilles and Tortoise Paradox. The paradox is Achilles and tortoise will have a race. The tortoise is given a head start say 100 meters. Suppose both started running at the same instant. It will take some time for Achilles to run the 100 meters. In this time the tortoise will have moved ahead say 10 meters. Then Achilles will need a further time to catch up the tortoise. When Achilles reaches the next point the tortoise has moved a further small distance. So, when Achilles reaches some point the tortoise has reached, he will have to go farther. Therefore, Achilles need to go to infinite number of points to overtake the tortoise, which, is impossible. So, he will never overtake the tortoise.

In reality commonsense says this cannot be, Achilles will easily overtake the tortoise. Therefore this is a paradox.

Is it? The problem is that we assume that space and time are continuous entities which can be divided indefinitely. It is not so. Time and space are discrete. The locomotion is not a smooth one where it can be divided in to infinitely. The movement is in jumps. At one stage Achilles will jump over the tortoise.