Zeno’s paradox only seems like one before you learn differential Calculus.
That’s because dx is going to zero, true, but as dt goes to zero.
We have figured out that this converges to an actual number, in a system that is totally consistent and makes sense.
x0 + sum of all the dx converges to x1 just as t0 + the sum of all the dt converges to t1. And that’s the exact time when Achilles catches up to the tortoise.
Zeno’s paradox ignores that dt is going to zero, and always acts like the sum of all the dt is infinity, thus “Achilles will never reach the tortoise” is wrong.
That’s because dx is going to zero, true, but as dt goes to zero.
We have figured out that this converges to an actual number, in a system that is totally consistent and makes sense.
x0 + sum of all the dx converges to x1 just as t0 + the sum of all the dt converges to t1. And that’s the exact time when Achilles catches up to the tortoise.
Zeno’s paradox ignores that dt is going to zero, and always acts like the sum of all the dt is infinity, thus “Achilles will never reach the tortoise” is wrong.
Simple!