#MathsInMinutes Day 38: Zeno´s Paradox

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Zeno´s paradox is one of several paradoxes posed by Greek mathematician Zeno of Elea, in the fifth century BC:

Tortoise and Hare are running a race over a two-mile track. Hare runs off at a steady pace. Tortoise, being a philosophical creature, sits down, safe in the knowledge that Hare will never arrive at the finishing line.

First, thinks Tortoise, Hare has to run a mile, then half the final mile, then half the final half-mile, and so on. Surely it is impossible for Hare to cover this infinite number of distances?

Zeno´s paradox raises both mathematical and philosophical issues. From a mathematical point of view the key point is that, in some cases, infinite sequences of numbers produce summed series that converge to a finite value, so if this is true for the distance covered and the time taken to cover the finite distance, then the Hare should arrive without any problems. 

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