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 is that it would take an infinite number of steps.
As many later philosophers and mathematicians pointed out, this infinite number if steps (catching up to each position the tortoise was at previously) takes a finite amount of time, so there is no paradox in Achilles passing the tortoise at some finite time.
However, a response has been made that the problem is not with the simple kinematics of the situation, but the fact that such an infinite subdivision is possible – for continuous motion to take place we are forced to assume that a completed infinity exists and we can traverse it. So if you add that premise explicitly (the infinity of the continuum cannot exist) you can still conclude that motion is impossible, and whatever we perceive is some form of illusion.
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