China DOS Union

The tortoise and the hare are having a race. The tortoise runs 10 meters first, and then the hare starts running. When the hare reaches the 10-meter point, the tortoise has moved a little farther ahead. When the hare reaches the tortoise's new position, the tortoise has again moved a little farther ahead. And so on. In this way, the hare can only get infinitely close, but can never pass the tortoise. This obviously does not match the facts. So where is the problem? According to this theory, for any two objects, if there is an initial displacement difference, the faster one can never catch up with the slower one. So where exactly is the mistake?

sorry, this isn't a logic puzzle, it's a paradox.

I give up, I can't make sense of the question.

Oh, I get it now... This problem is in my math textbook!

What do you understand? Tell us.

The explanation given in the original English version of that problem is like this:

In the fifth century B.C., the Greek philosopher, Zeno of Elea, posed four problems, now known as Zeno's paradoxes. These problems wre intended to challenge some of the then-current ideas about space and time.

And then comes this problem.

yes! But you still haven't told everyone what it is that you understood.

Because the finish point is always set by the tortoise. The hare can only pass an existing reference point, but that reference point is always being updated over time. For something that hasn't happened yet, the question of surpassing it can't exist, unless that hare can outrun time.

Exactly..

KO, don't forget to post the answer!!!

What nre said makes sense. The reason is that this problem doesn't take time into account, only position. For example, the hare reaches the tortoise's new position in one second, while the tortoise took a full minute, and by then who knows where the hare has already gone. So they are being compared over unequal times. Unless time doesn't exist.

Let me correct that a bit. It should be understood this way: within a certain specific time range, the hare cannot catch up with the tortoise. Because the problem is like this: when the hare gets infinitely close to the tortoise, time at that moment is also getting infinitely close to zero. In other words, time has come to a standstill.
For example, the hare takes 10 seconds to run the 10 meters that the tortoise got as a head start, and during that time the tortoise runs 1 meter. Then the hare takes 1 second to run that 1 meter, while the tortoise runs 0.1 meter; then the hare takes 0.1 second to run 0.1 meter, while the tortoise runs 0.01 meter; then the hare takes 0.01 second to run 0.01 meter, while the tortoise runs 0.001 meter.......
In that case, time starts getting infinitely close to zero. That is to say, within 11.111111....... seconds, the hare cannot catch up with the tortoise. But if it goes beyond that time, even by just a tiny bit, the hare passes the tortoise.

It's just a limit problem!

This is a limit problem.

10*（1+1/10+1/100+……）
Within the limit, the hare definitely can't catch up with the tortoise, but once past that limit, the hare can pass the tortoise.

This is switching concepts.
It's swapping the concept of infinite space with the concept of infinite time...
A distance problem is a spatial problem.
Whether it can catch up or not is a time problem.