Re: Post your Best/Latest Accomplishment
The paradox is that by the time the hare reaches the point where the tortoise used to be, the tortoise has already moved forward.
The second one is more intuitive (and also more relevant.) Suppose you want to move 10 feet. In order to get there, you must cross the halfway point, which is 5 feet. Once there, you must once again cross the new halfway point, 7.5 feet. You can continue to subdivide the remaining distance as many times as you want.
Both paradoxes rely on subdividing time or space infinitely. But just because a sequence is infinite it doesn't mean its sum is infinity. 10/2 + 10/4 + 10/8 + 10/16 + ... adds up to 10. It's obvious that you can move 10 feet regardless of the fact that you can subdivide 10 feet infinitely. The hare will still pass the tortoise.
Wouldn’t that only apply if the hare is trying to ‘catchup’ to the tortoise oppose to passing him to get to the finish line first?
The second one is more intuitive (and also more relevant.) Suppose you want to move 10 feet. In order to get there, you must cross the halfway point, which is 5 feet. Once there, you must once again cross the new halfway point, 7.5 feet. You can continue to subdivide the remaining distance as many times as you want.
Both paradoxes rely on subdividing time or space infinitely. But just because a sequence is infinite it doesn't mean its sum is infinity. 10/2 + 10/4 + 10/8 + 10/16 + ... adds up to 10. It's obvious that you can move 10 feet regardless of the fact that you can subdivide 10 feet infinitely. The hare will still pass the tortoise.
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