| dtewi said: In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 feet, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, for example 10 feet. It will then take Achilles some further period of time to run that distance, in which period the tortoise will advance farther; and then another period of time to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. This seems like a very interesting topic. If infinity can not be reached, he can not pass. Or maybe infinity is reached, and he is able to overtake. What is the solution? How can Achilles overtake the Tortoise? |
I like this question, it made me think, i say for achilles to change his walking/running speed, if he doesn't he will never surpass the tortoise. BUT it is mentioned that at the time it took achilles to cover the 100 foot gap, the tortoise has ran an extra 10 feet, which leaves it at 100 feet -Achilles, 110 Feet -Tortoise. Achilles would of past the tortoise, since Achilles is running at a fast pace, while the Tortoise is running at a slower pace. Now it would of been different if the tortoise got a headstart of a hundred feet, and Achilles and the Tortoise ran at the SAME constant speed, then it will be impossible for Achilles to overtake the Tortoise.
@the highlighted part, Due to this information, it is possible for Achilles to overtake the Tortoise, at some point
