Answering Achilles' knowledge of calculus can't catch up with the tortoise. I am a liberal arts student. I ask God to help me not to paste the online theory and answer it step by step.

You can't type the formula directly, but the following explanation is very clear. If you have to apply the limit formula, you can directly bring it in yourself.

This paradox has a wrong premise in mathematics: mistakenly think that the sum of infinite numbers (finite numbers) must be infinite.

First of all, every time you chase a turtle, you need less and less distance. Secondly, this process will be repeated countless times, which means that * * * has countless such journeys.

What we want to ask is: What is the sum of these infinite journeys? Is it positive infinity?

For example, the first time I chased a turtle, I walked 1m, the second time I walked half a meter, and the third time I walked a quarter of a meter. .........................

So what is the total distance of1+0.5+0.25.125? ................

If it is equal to infinity, it means that the situation of not catching up with the tortoise can be maintained from 0m to positive infinity, in other words, it will never catch up with the tortoise, which is the paradox.

If it is equal to a finite number, that is, equal to X, it means that the situation of not catching up with the tortoise can only be maintained at a distance of X meters from the starting point. In other words, you can not only catch up, but also meet and surpass the tortoise at x meters.

Can infinite numbers be finite numbers? We know that the summation of infinite series in mathematics is to answer this question, and once the series converges, the result is bound to be limited.

Simply put, in the turtle-chasing model, it can be proved that the sum of all distances must be limited, that is to say, it must be caught up.

Author: Han Tangtian

Link:/question/51195954/answer/124909672

Source: Zhihu.