zeno's paradox of achilles and the tortoise zeno's paradox of achilles and the tortoise goes like this achilles is chasing after the tortoise as achilles is much faster than the tortoise you would expect him to eventually catch the tortoise zeno asks us to consider the following idea however to catch the tortoise achilles has to first reach the torch's starting point by the time he gets there however the tortoise will have moved forward out of achilles reach achilles now has to reach the tortoise's new point but again by the time he gets there the tortoise will have moved forward this keeps happening forever each time achilles reaches the point where the tortoise was the tortoise will have moved forward out of the way hence achilles will never catch up zeno used this paradox as evidence that motion does not exist is just an illusion let's put some numbers to this and see what happens suppose the tortoise is 0. 9 meters ahead of achilles the torso is traveling at 0. 1 meters per second while achilles is running at 1 meters per second basic mass tells us that after 1 second they will both have reached the 1 meter mark and achilles will have caught the tortoise now let's look at it from zeno's point of view to reach the tortoise's starting point achilles needs to run 0.
9 meters in this time the tortoise will have travelled 0. 09 metres achilles now needs to travel this 0. 09 metres but meanwhile the tortoise will have travelled 0.
009 and metres ahead this continues infinitely we can see that achilles reaches the first point at 0. 9 meters then 0. 99 metres 0.
999 metres and so on to zeno because achilles has an infinite number of finite ketchups to make he can never actually catch up to the tortoise but we have seen if achilles can reach one meter he will have caught the tortoise so can he reach one meter the answer is yes with the benefits of modern mathematical analysis which did not exist in zeno's time we know that the limit of 0. 9 plus 0. 09 plus 0.
009 and so on equals 1.
