Tortoise and Achilles

The Tortoise challenged Achilles to a race, claiming thathe would win
as long as Achilles gave him a small head start.
Achilles laughed at this, for of course he was a mighty warriorand swift
of foot, whereas the Tortoise was heavy and slow.

How big a head start do you need? he asked the Tortoise with a smile.
Ten meters, the latter replied. Achilles laughed louder than ever.
You will surely lose, my friend, in that case, he told the Tortoise,
but let us race, if you wish it.
 
On the contrary, said the Tortoise, I will win, and I can prove it to you
by a  simple argument.
Go on then, Achilles replied, with less confidencethan he felt before.
He knew he was the superior athlete,but he also knew the Tortoise
had the sharper wits, and hehad lost many a bewildering argument
with him before this.

Suppose, began the Tortoise, that you give me a 10-meterhead start.
Would you say that you could cover that10 meters between us very quickly?
Very quickly, Achilles affirmed.
And in that time, how far should I have gone, do you think?
Perhaps a meter, no more.
 
Very well, replied the Tortoise, so now there is a meter between us.
And you would catch up that distance very quickly?.
Very quickly indeed!
And yet, in that time I shall have gone a little way farther,so that now
you must catch that distance up, yes?

Ye-es, said Achilles slowly.
And while you are doing so, I shall have gone a little wayfarther, so
that you must then catch up the new distance,
the Tortoise continued smoothly.
Achilles said nothing.
And so you see, in each moment you must be catching up the distance
between us, and yet I at the same time will beadding a new distance,
however small, for you to catch up again.
 
Indeed, it must be so, said Achilles wearily.
And so you can never catch up, the Tortoise concluded sympathetically.
You are right, as always, said Achilles sadly and conceded the race.