How does the Achilles and the Tortoise paradox work? Isn’t Achilles bound to take over the tortoise after a certain point?
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The paradox appears to arise because if you split the race into an infinite number of slices of time and add them together it would appear that by adding together an infinite number of values you would get a result that is also infinite.
Which seems intuitive. Paraphrased – “keep adding on a little more each time for infinity times and the end result cannot be finite” – it makes sense. But it’s wrong. They knew it was wrong, but couldn’t explain why, so they had this paradox where Achilles will obviously catch up with the tortoise, but they also had an apparently logically way of describing the process that made it seem like catching the tortoise is impossible.
The solution is in an area of math called Limits, and they were asking all the right questions to get to figuring out Limits, but eventually it took around two thousand years to discover the math to explain what was happening.
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