Before reaching the destination, one should walk the distance of 1/2, then walk the remaining total distance of 1/2, and then walk the remaining 1/2 ... According to this requirement, one can walk indefinitely. So there are two situations: ① this person has not started at all; As long as he starts, he will never reach the finish line. (although it is getting closer and closer to the finish line)

2. Achilles paradox

In fact, this paradox refers to this interesting story-Achilles and the tortoise race. Achilles is a hero who is good at running in ancient Greek mythology. In the race with the tortoise, his speed is 10 times that of the tortoise. The tortoise runs in front of 100 meters. He chased after him, but he couldn't catch up.

3. The arrow does not move

The "arrow" in "the arrow does not move" refers to the arrow in the bow and arrow. Normal archery, as we all know, can fly out and reach another position as long as the arrow leaves the string and moves in space for a period of time.

However, Zhi Nuo believes that if we intercept every moment of the "arrow", it will be "still" in the air. Since every moment is static, all moments should be static, so the "arrow" is "motionless".

4. March, March, March

Suppose on the playground, at an instant (a minimum time unit), queues B and C move to the right and left by a distance unit respectively.

At this point, relative to b, c moved by two distance units. Zhi Nuo thinks that since a queue can move by one distance unit (minimum time unit) in an instant, or by one distance unit in half a minimum time unit, then half a time unit is equal to one time unit.

Extended data

Aristotle explained Zeno's paradox like this:

For the first and third paradoxes, he thinks that as long as time is infinitely inseparable, then each time point corresponds to a space point, and we can travel through an infinitely inseparable space in an infinitely inseparable time period.

For the second paradox, he thinks that when the distance between the pursuer and the pursued is getting smaller and smaller, the time required for catching up is getting smaller and smaller. The sum of infinite smaller and smaller numbers is limited, so you can catch up in a limited time. (However, it is not rigorous)

For Achilles paradox, Archimedes found a method similar to the summation of geometric series. The time required in the problem is exponentially decreasing, which is a typical geometric series, so it can be seen that the total time for Achilles to catch up with the tortoise is a finite value.