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I dare say that Zeno simply did not know that the sum of an infinitely decreasing geometric progression is equal to a finite number. Imagine a certain distance as a segment equal to 1. The turtle is in the middle of the segment, that is, it has passed 1/2. Achilles is just beginning his journey and is at the very beginning. Then Achilles passes 1/2 and the turtle 1/2 + 1/4, Achilles passes 1/2 + 1/4 and the turtle 1/2 + 1/4 + 1/8 etc. As a result, we get that 1/2 + 1/4 + 1/8 + 1/16+… = a finite number, namely 1. In the end, both Achilles and the turtle will pass the distance = 1 and they will be equal.

Commentators have already explained

the paradox of Achilles and the tortoise, i.e. Achilles cannot catch the tortoise (apparently, ninja, she even Achilles can overtake), as Achilles will have to run half way up the turtle, and then half way halfway to the turtles, and then halfway halfway halfway to the turtles, and so on (I hope I've explained clearly), that is, Achilles cannot catch the tortoise.But the fact is that

this paradox still has an end. As long as Achilles catches up with the turtle, it will come to the point that there will be a distance of two atoms between them, after a while and one atom,BUTas we know from the course of the school curriculum (Svyatoslav, 15 years old), an atom is an indivisible particle. That is, Achilles has no other choice but to simply run through this atom, and then catch up (and therefore overtake) a fast turtle.I also suggest you watch a video on this topic (with the voice acting of the problem, I agree, the main thing is to catch the meaning):

http://www.youtube.com/embed/Nhg03Rs8eLo?wmode=opaque

I am an expert, I have completed nine classes, you can trust me)))

Turtle Paradox This paradox was coined by the ancient Greek philosopher Zeno. Its essence is as follows: suppose that Achilles runs 10 times faster than the turtle and is 1000 steps away from it. While Achilles will run 1000 steps, the turtle will crawl another 100 steps. When Achilles runs 100 steps, the turtle will crawl another 10 steps, and so on ad infinitum. As a result, Achilles will never catch up with the turtle. Naturally, we all understand that in real life, he would probably catch up with her and overtake her.

The paradox can be explained by the fact that in reality space and time cannot be divided indefinitely.

There lived in Other Greece a merry little Zeno (about 500 BC). He amused himself by inventing various paradoxical situations and reasoning about various physical processes and concepts, called aporias. One of the nine preserved ones is “Achilles and the Turtle”, meaning that while Achilles runs a hundred meters that separates him from the turtle, the turtle will crawl 10 meters. While Achilles runs these 10m., the turtle will crawl 1m. Achilles – 1m, turtle 10cm. And so on endlessly. That is, Achilles will never catch up with the turtle, always there will be some microscopic distance between them. The mistake (consciously made in Zeno's reasoning) is that neither motion nor objects divide, especially infinitely. You can't treat Achilles as an abstract point. The turtle, too. They have very specific dimensions.