For those of you who aren’t familiar: Achilles and a Tortoise race, however the tortoise is given a leading start. Achilles is at Point A, whereas the tortoise is ahead at point B. The race begins, and by the time Achilles makes it to point B, where the Tortoise used to be, it has reached point C. Then Achilles arrives at point C with the Tortoise at point D. So on and so forth, with Achilles never catching up to the Tortoise as per the paradox.
But he definitely catches the Tortoise eventually, right? The tortoise has a lower velocity, hence the head start, so after a certain amount of time the distance between points is smaller than Achilles and the Tortoise’s difference in speed. What, if anything, is paradoxical about the world’s most famous paradox?
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The basic solution to the paradox is integral calculus. The normal statement of the paradox keeps using smaller and smaller time intervals. Integral calculus lets you take an infinite number of infinitely small areas and have it add up to a finite answer. (Which is scary at first, but you get used to it pretty quick.) Once you have that insight, the paradox goes away and the normal view of velocity versus time gets strengthened.
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