system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why does the paradox of motion (ie. Achilles and the Tortoise) seem so plausible but still have no relevance in physical reality?

Why is it that motion is possible at all even when a seemingly plausible thought experiment can almost convince you it'd impossible? No doubt that numbers can get infinitely more small in value, shouldn't the same hold up for distance?

Explain like I'm 5 (if you dare)

Edit: Wow, thanks for those explanations, I never really questioned the fact that the story only gets told up to a certain point.
gpt
The paradox, for those who don't know, says that Achilles is in a race with a tortoise

He gives the tortoise a head start. Then he starts. Of course, he's much faster than the tortoise, so he ought to easily catch and pass it.

The paradox is that, when he starts, he notices that the tortoise is a certain distance ahead of him, so he runs to this point. Then he sees that the tortoise has moved further, so he runs to the point to where the tortoise is now. Again, when he gets there, the tortoise is no longer there, so again he looks at where the tortoise is, and runs to there, and so on..... and he never actually catches the tortoise.

The reason this is false, is that each time, the distance he has to run to where the tortoise was gets smaller and smaller, tending towards zero. The time taken to run that distance also gets smaller and smaller, tending towards zero. If we add up all these distances, they will get closer and closer to a certain point - but Achilles, using the running style described in the paradox, will never get past a certain point.

This certain point is the point where he will overtake the tortoise.

What the paradox does is pick an infinite number of points, getting closer and closer together, but all of them *before* the point where he overtakes the tortoise. Because it omits any point at or after where the overtake happens, it misses a big part of the story... and that's why it's not true.