Can tortoises and haunts catch up new Why hare can never catch up with tortoises

This is the famous proposition of Zeno, the wise man of the ancient Greek sophists, that Achilles could not outrun the tortoise. How could Achilles not be able to outrun the tortoise? Zeno divided the process infinitely, and his idea was:

Achilles was some distance from the tortoise in front of him, and during the time he had finished the dam the tortoise had gone some distance further, so he ran the second distance again, and in that time the tortoise had advanced some more distance, and it was the same for the rest of the time, and it was impossible for Achilles to catch up with the tortoise.

But if you think about it, you will understand that the distance between Achilles and the tortoise is shrinking, the distance they chase is close to zero in each segment, and the time for Achilles to catch up with each distance is also close to zero, and catching up with the tortoise is a limit, but time has not passed like this, time is linear and evenly flowing, and it will not become less and less. So Zeno's hypothesis is that when time is infinitely close to the zero point of catching up, Achilles can't outrun the tortoise.

You have to develop depending on the problem, have you ever studied calculus, if you have learned calculus, you will know that the limit can be caught up.

You know, the limits are infinitely close, so you can catch up.

This is a paradox, and what seems complicated is actually a mistake in language.

When it comes to the topic, time is the first nature.

Matter determines time, without matter there is no time, matter is the first nature.

Therefore, when their distance is only the distance from the primordial, it cannot be measured by time, because absolute time is based on the primordial object, and the primordial is in motion, so time can also be relatively stationary while matter is in motion at this time.

Maybe you can't understand it, but if you look at the general theory of relativity, you can see that the question itself is wrong, and of course there is no correct answer.

It's a paradox, so why torture yourself? When you're about to catch up, take a big step forward and catch up.

What are your criteria? It's speed, not distance. Don't forget the time.

This is a paradox.

Simply talking about running, who will win the tortoise and rabbit race? The answer, of course, is rabbits, because rabbits run faster.

The rabbit tells the tortoise to run for a while and then chase it; Assuming that the runway is very long, will the rabbit win or the tortoise will win at this time?

On the whole, you can see at a glance that this is a simple catch-up problem, and it is definitely the rabbit that wins, because the rabbit is always much faster than the tortoise, and even if the tortoise runs a little first, it will still catch up. It is only a question of when to catch up, not whether to catch up or not.

But will it catch up? Let's discuss::

The tortoise first runs some distance and is denoted as A1, and then the hare also starts running and starts chasing the tortoise; At this time, the turtle must be ahead of the curve.

When the rabbit chased to the place of A1, the tortoise was certainly not idle, and must have run some way forward, assuming that this part of the journey is A2; At this time, the tortoise ran A2 more distance than the rabbit, and the tortoise was still in front of the rabbit.

Of course, the rabbit will not stop, and continues to chase - and ran the A2 distance again, but the turtle continues to run, and in this period of time it has run so far as A3, still in front of the rabbit.

From A3, A4 all the way to An, and until to N-- infinity, there will be such a conclusion: the tortoise is in front of the rabbit - to express it mathematically: the distance that the tortoise runs every time is recorded as an, and when the distance that the rabbit runs is an, the tortoise has already run to the a(n+1) distance, and when n tends to infinity, this conclusion still holds, and the tortoise is always in front of the rabbit.

First of all, I can say very clearly that this is not a paradox. It has a very clear and unambiguous explanation.

——1.The tortoise will move forward when the rabbit catches up with the tortoise, and as they get smaller and smaller, the rabbit will trace it for a shorter and shorter time, eventually approaching lim t = 0

2.In the time of limt=0, the rabbit really can't catch up. Because it takes time to chase and you don't give the rabbit a lot of time, how can it catch up?

3.When tlim, the rabbit can catch up with the tortoise.

What do you think? It's not a paradox, it's a matter of time that will eventually catch up.

The person who invented this question – IMHO – is a bit childlike in mind.

Taking the tortoise as a reference frame, the speed of the tortoise is 0, and from the tortoise's point of view, the rabbit approaches the tortoise at a uniform speed with the speed difference between the two, so there is a moment when it reaches the tortoise's position and surpasses the tortoise.

There are two kinds: the first is that the tortoise runs to the finish line and the rabbit cannons, and the second is that the rabbit sleeps halfway.

This is a famous mathematical paradox!

While the rabbit is running, the tortoise is also running ......If a rabbit is twice as fast as a tortoise, their catch-up relationship looks something like this:

Rabbit |Turtle |Although the gap between them is getting smaller and smaller, there is always a gap, but this is not possible in reality, and there is no need to waste brain cells thinking too much about this kind of ......

He was too careless, underestimated the other party, and was too arrogant.

This question comes from the "tortoise-hare paradox".

The content is: The tortoise has climbed some distance and is in the point A position, at which point the rabbit wants to catch up with the tortoise from behind. However, while it was chasing the tortoise, the tortoise was still crawling forward.

Therefore, if the rabbit wants to catch up with the tortoise, it must first reach point A, where the tortoise started. But when the rabbit reached point A, the tortoise climbed another section to point B. Then the rabbit has to chase to point B, but at this time the tortoise has reached point C, and the rabbit has to reach point C if he wants to catch up with the tortoise, but the tortoise has already climbed to point D...... at this timeAlthough the distance between the rabbit and the tortoise will be close to infinitesimal in this way, the hare will not be able to catch up with the tortoise in any case.

The "Tortoise and Hare Paradox" evolved from the "Achilles and Tortoise Race Paradox" proposed by the ancient Greek philosopher and sophist "Zeno". Since this conclusion does not correspond to common sense, it becomes a paradox.

In fact, in this paradox, it is not a question of racing at all. The race is about the common goal of the participants. However, in the tortoise-hare paradox, there is no such common goal at all.

The end of the race in the tortoise-hare paradox is actually the tortoise itself, not the goal other than the tortoise-hare paradox. This is the first place where the illusion arises.

In the tortoise and rabbit paradox, because there is no common end, the end is the tortoise itself, so that as long as the tortoise turns around, the hare is behind it. Of course, it will never be able to catch up.

Let's assume that a second can be divided into many segments, each of which is set to x, and that the distance can be divided into many segments, each of which is set to y.

Suppose a rabbit can run two y's in one x time, and a tortoise can only run one y in one x time, (because a rabbit is faster than a tortoise).

Then when the rabbit chases the tortoise, it chases the tortoise until it is only a distance of y. In the next x time, the rabbit runs two Y's, the turtle runs one Y, and the rabbit directly overtakes the turtle at this x time. And then it's more and more over the tortoise.

In fact, this so-called refutation also proves a truth, that is, time, space, and any matter cannot be divided infinitely, because when it is divided to the limit, there is only one smallest unit left. In this one unit of time, the rabbit jumped directly from behind the tortoise to in front of the tortoise.

The reason why the rabbit can't catch up with the tortoise is because in this problem time can be divided infinitely, while in reality the rabbit can catch up with the tortoise, so it can be concluded that time has a minimum unit and cannot be divided indefinitely.

The distance between the rabbit and the tortoise is getting smaller and smaller, the distance is getting closer to infinitesimal and the rabbit is faster, and the rabbit catches up with the tortoise.

The thousand-year-old king is an eighty-thousand-year-old tortoise, and a hundred-year-old rabbit is not chased.

"Millennial King Eight, 10,000-year-old turtle" is a relatively exaggerated statement, which means that the lifespan of turtles and turtles is very.

Long. It is to explain the meaning of hidden longevity and long time.

Originally, it was not a derogatory meaning, but it was just a description of the turtle king eight who lived a long time.

But because many curses are now associated with Wang Ba and the turtle, the meaning of the word has changed somewhat.

Both the king and the turtle are long-lived, and the thousand-year-old turtle is even more rare and precious.

Rabbits are usually not long-lived, and rabbits that have lived for 100 years are very abnormal, and people avoid them when they see them. I'm worried about attracting bad simple search things.

Categories: Entertainment & Leisure >> brain teasers.

Problem description: Tortoise and rabbit race, assuming the tortoise runs out first, the hare will never be able to catch up! Why is that?

Analysis: This is a famous mathematical paradox!

While the rabbit is running, the tortoise is also running ......If a rabbit is twice as fast as a tortoise, their catch-up relationship looks something like this:

Rabbit |Turtle |

Although the gap between them is getting smaller and smaller, there is always a gap, but this is not possible in reality, and there is no need to waste brain cells thinking too much about this kind of ......

1.The rabbit was dumbfounded before the finish line, and it wasn't to rush over, and it wasn't to go over, anyway! It's a lost game!

Because there is a woodblock before the end of the line, which says: The turtle came first) 2This is a kung fu turtle who knows ninjutsu and won the championship by using the "Earth Escape Method" 3

Because Mr. Turtle ate a whole bunch of "Mexican jumping beans!" ” 4.This long tortoise and rabbit race uses the latest game rules:

Run backwards! (The rabbit says, "Wow!")

I'm not going to jump backwards! ”）5.The rabbit, who loves science, seriously discussed "gravity" with Newton under the apple tree.

It ......It forgot that the game was still ......It's not over yet. 6.Because the rabbit picked up the leftover elixir that Chang'e ate when she went to the moon, she jumped on the moon lightly.

7.The rules of the contest are: "Guess a punch and take a step."

The rabbit's luck has faded to the house, and he has not won from beginning to end. 8.The lucky turtle picked up the Aladdin's magic lamp, and its first "little" wish was:

Beyond that big-eared mammal. ” 9.One step further and the rabbit is the champion.

But it is too superstitious to think that the rabbit that crosses the black cat will be unlucky for the rest of its life. 10.The tortoise mixed the rabbit's carrot juice with a "delirium."

The rabbit climbed the tree like a woodpecker and said, "I am a little bird." ”）

As long as the tortoise runs first, there must be some distance between it and the rabbit. In order for a rabbit to catch up with a tortoise, the rabbit must first pass through the "midpoint" of their distance, and when the rabbit passes through this midpoint, the next "midpoint" will appear at the same time, and so on. The rabbit can only get infinitely close to the turtle, but it can never catch up.

Scientific Explanation:

The beginning of the race is neglected, starting from the rabbit waking up; If the tortoise is 100 meters in front of the rabbit, and now the rabbit starts chasing the tortoise, when the rabbit chases 100 meters, because the tortoise is also running (although it is very slow, but for the sake of clear description, let's assume that the tortoise runs to the 150th meter, that is, it is 50 meters in front of the rabbit), when the rabbit catches up with the tortoise at 150 meters, the tortoise goes forward again, and when the rabbit catches up with the tortoise again, the tortoise is still moving in front of the rabbitIn this way, although the rabbit is infinitely close to the tortoise, it can never catch up, so the tortoise and the hare race, and the winner is the tortoise, hehe: o4 k0 u* p% m+ n*

Although this explanation does not match the situation in reality, but you can never overturn it, if any master can prove it wrong, please write down the reason, thank you!

The tortoise is not working hard at all, he is not interested in competition and victory, the tortoise is just enjoying the fact that he is moving forward, this is the world that only the tortoise that lies on the ground and moves forward, in order to enjoy this wonderful world, the tortoise has been advancing, in the world of the tortoise, the rabbit no longer exists, and it is also because of this that the rabbit has not been woken up from sleep.

The rabbit runs because he looks down on the tortoise, and he wants to prove that he is very good.

In physics, there is a unit called "Planck distance", the minimum distance that an object can pass through without any time, that is, the object can exist in two places at the same time, so in this way, the rabbit can be the top of the tortoise!

You ignore the time factor, and you deduce that the "midpoint" of the intermediate medium is actually limiting the infinity of time.

time, space; Life, environment!

Running obstacles, the kind with ponds.