One of the paradoxes is famous: "? Achilles can't outrun the tortoise. " Achilles (also known as Achilles) is a hero who is good at running in ancient Greek mythology. He races with the tortoise, which is ten times faster than the tortoise, and the tortoise runs in front of 100 meters. He chased after him, but he couldn't catch up with the tortoise. Because in the competition, the pursuer must first reach the starting point of the pursued. By the time Achilles caught up with 100 meters, the tortoise had already climbed forward 10 meters, thus creating a new starting point. Achilles must continue to chase, and when he catches up with the tortoise's climb of 10 m, the tortoise has already climbed forward 1 m, and Achilles can only chase 1 m again. In this way, the tortoise will create an infinite starting point, and it can always create a distance between the starting point and itself, no matter how small the distance is, but as long as the tortoise keeps struggling to climb forward, Achilles will never catch up with the tortoise!
? It is explained that if the jogger is in front of the runner, the runner will never catch up with the jogger, because the chaser must first run to the chased starting point. When he reaches the chased starting point, the jogger moves forward for a period of time, and a new starting point is waiting for it. There are infinite such starting points.
In fact, according to the knowledge of the summation of infinite proportional recursive series learned in middle school, we can easily overturn Zeno's paradox by listing an equation: Achilles is running1000 (1+0.1.01+…………………………………………………………………………………………) =/kloc-. People think that the sequence ................................................................................................................................... of 1+0. 1.0 1+ is just an illusion.
We might as well calculate that the time for Achilles to catch up with the tortoise is t (1+0.1+0.01+..............) = t (1+kloc-0//9) =10t/9.
Zhi Nuo's statement that Achilles can't catch up with the tortoise hides the condition that the time must be less than 10t/9. Infinite subdivision does not mean that it will not flow from time 1 to time 2, otherwise your clock will stay at 59 minutes and 59.9999 ............ is always a second. The reason for Zeno's paradox is that "Zhi Nuo time" can't measure the phenomenon after Achilles catches up with the tortoise. After Zhi Nuo reaches infinity, normal timing can still be done, but Zhi Nuo's "clock" can no longer measure them. This paradox actually reflects that time and space are not infinitely separable and that motion is not continuous.
Achilles can continue to approach the tortoise, but he can't catch up before a certain point. But it is not true that we can never catch up with this result, because this paradox only makes us consider catching up with the previous distance, not catching up with the previous distance.