1 math story

Smiling and naughty are very friendly friends. They all use the same water meter. There are three people in Xiaoxiao's family and four in Naughty's family. Summer water consumption of two families 120 tons. The two families intend to pay by population. How much do 0.7 yuan, Xiaoxiao and Naughty have to pay for each ton of water?

2. One night, very late, an elderly couple walked into a hotel. They want a room. The receptionist replied, "Sorry, our hotel is full and there are no rooms." Looking at the tired appearance of the old couple, the waiter said, "But let me think ..."

At this point, do you want the following to be the continuation of mathematics or the end of literature? But in any case, mathematics and literature will break up here.

The story of mathematics goes like this: the kind waiter began to solve the room problem for the old couple: he woke up the guests who had already slept in the hotel and asked them to change places: 1 The guest in room 2 changed to room 3, and so on until each guest moved from his room to the next room. ?

Then a miracle happened: 1 The room was empty. The waiter happily arranged the old couple in. There are not many rooms and many guests. When the two old people arrived, all the rooms were crowded with guests-but just move each guest to the next room and the first room will be empty. Why? It turned out that two old people entered the mathematically famous Hilbert Hotel-it is considered to be a hotel with countless rooms.

The story of literature goes like this: the kind waiter led the old couple to a room and said, "Maybe not the best, but now I can only do this." The old man saw that this was actually a neat and clean room and lived happily. The next day, when they came to the front desk to check out, the waiter said to them, "No, because I just lent you my room for one night-have a nice trip!" " I see. The waiter stayed up all night, so he stayed at the front desk all night. The two old people were very moved. The old man said, "Son, you are the best hotel manager I have ever seen." You will be rewarded. "The waiter said with a smile, it's nothing. He sent the old man out, turned around and went on doing his own thing, and forgot all about it. Unexpectedly, one day, the waiter received a letter with a one-way ticket to new york and a short postscript, inviting him to accept another job. He flew to new york and reached a place according to the route indicated in the letter. When he looked up, a magnificent hotel stood in front of him. It turned out that one night a few months ago, he received a billionaire and his wife. The rich man bought a big hotel for the waiter, convinced that he would manage it well.

? Guess what?

The story of mathematics is told by the great mathematician david hilbert, who introduced the concept of infinity into mathematics. This concept is very important to this subject. It can be said that without it, it is difficult for us to imagine how mathematics would exist. As long as anyone who can count knows, every number has a successor until infinity (so in Hilbert Hotel, there will be a successor behind every house until infinity) ... Mathematics is a science about infinity.