Topic: Puzzle 11

+ Puzzle 11
From	Message
Damo 10 Feb 03, 22:02	+ Puzzle 11 Suppose that the swift Achilles is having a race with a tortoise. Since the tortoise is much slower, she gets a head start. When the tortoise has reached a given point A, Achilles starts. But by the time Achilles reaches A, the tortoise has already moved beyond point A, to point B. And by the time Achilles reaches B the tortoise has already moved a little bit farther along, to point C. Since this process goes on indefinitely, Achilles can never catch up with the tortoise. How can this be?
VALLEY 11 Feb 03, 11:27	+ Puzzle 11 Achilles is moving at the same speed as the tortoise?
Jon 11 Feb 03, 20:03	+ Puzzle 11 Achilles is an asymtote. He never actually reaches the tortoise ever!
Rich_Rocks 11 Feb 03, 20:51	+ Puzzle 11 Achilles is also a tortoise.
Sweetmadness 12 Feb 03, 22:40	+ Puzzle 11 I don't know....why do you ask??
Damo 12 Feb 03, 22:43	+ Puzzle 11 The question does say that Achilles is 'swift' and that the tortoise is 'much slower'
VALLEY 14 Feb 03, 08:32	+ Puzzle 11 The infinite series of fractions involved in e.g., the Racetrack, has a finite sum: (1/2 + 1/4 + 1/8 + ...) = 1. Hence one will of course reach the end of the track. Of course half the length, plus one fourth, plus one eighth, and so on, add up to the whole length. And that's just the point. The whole length contains an infinite number of finite parts. In order to traverse it, therefore, a runner would have to complete an infinite number of tasks. But how can such a thing to be possible? It isn't! Is that right?
Damo 14 Feb 03, 23:48	+ Puzzle 11 Pretty much along the right lines. What you haven't done is explain it in terms of Achilles and the tortoise
VALLEY 15 Feb 03, 15:55	+ Puzzle 11 Well you know what i mean!
spookylukey 19 Feb 03, 00:32	+ Puzzle 11 Achilles will pass the tortoise after a finite amount of time, because he is going faster. You can of course break this time into an infinite number of steps, each step getting smaller and smaller, as described, but this doesn't make any difference - you can still complete a infinite number of things in a finite time.
Jon 19 Feb 03, 20:52	+ Puzzle 11 asymtote You un cultured muppets
VALLEY 19 Feb 03, 22:20	+ Puzzle 11 I think my answer is right...........hang on, i alreadd wrote this message. Someones erased it! HEY!!!!
Jon 20 Feb 03, 20:17	+ Puzzle 11 Actaully I answered it in one word.... but no... I was ignored!