How could a humble tortoise beat the legendary Greek hero Achilles in a race? The Greek
philosopher Zeno liked a challenge and came up with this paradox. First, the
tortoise is given a slight headstart. Anyone fancying a flutter would still
rush to put their money on Achilles, but Zeno pointed out that to overtake him
Achilles would first have to cover the distance to the point where the tortoise
began. In that time the tortoise would have moved so Achilles would have to
cover that distance, giving the tortoise time to amble forwards a bit more.
Logically this would carry on forever. However small the gap between, them the
tortoise would still be able to move forward while Achilles was catching up,
meaning that Achilles could never overtake. Taken to an extreme,
this bizarre paradox suggests that all movement is impossible but it did lead
to the realisation that something finite can be divided an infinite number of
times. This concept of an infinite series is used in finance to work out mortgage
payments, which is why they take an infinite amount of time to pay off.