Achilles and the Tortoise

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 head start

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 forwards

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 realization

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!