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Achilles and the tortoise and the Dichotomy paradox solved.

These two famous paradoxes are created by a Greek philosopher called Zeno, born in 490 B.C.
Achilles and the tortoise has two different types of approach:-

Achilles and the tortoise approach: This is where Achilles and the tortoise race against each other, however as we know an athlete like Achilles will over take the tortoise in no time; hence the tortoise was given a handicap. This is were the paradox plays in; Zeno argues that Achilles will never reach the tortoise. Achilles always manages to run to the point where the tortoise was previously, but by the time he reaches that point the tortoise has moved a little bit further away. For at every moment the tortoise is somewhere and Achilles is somewhere; and neither is ever twice in the same place while the race is going on. Thus the tortoise goes to just as many places as Achilles does, because each is in one place at one moment, and in another at any other moment. Therefore Achilles will never reach the tortoise.
Fig 1: Illustration of Achilles and the tortoise
“In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.”
—Aristotle, Physics VI:9, 239b15

Dichotomy approach: Is where Zeno claims that Achilles will never reach the tortoise. Basically