The Boschernitsyn theorem

In this paper we give a simple proof that the mapping of a compact metric space into itself that does not reduce distance is an isometry.
 
 
 
Display
The Boschernitsyn theorem
metric space with the metric of

are called isometries if for any

the equality
is valid.
. We shall prove the following assertion here:
 
 
Theorem. If

mapping of a compact metric space into itself, such that
 
 

 
 
for ...
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Friday PHP-quiz: a little adventure of the programmer Brad, one strange sequence and

Friday PHP-quiz: a little adventure of the programmer Brad, one strange sequence andprizes.Hello! We promised to do: we continue the series of mini-quizzes devoted to different programming languages ​​in our blog (previous: 1 (for knowledge of Python, PHP, Golang and DevOps) , .2 (completely Go) ). Today's issue is dedicated to PHP.  Under the cut - eight questions, a few adventures of the programmer Brad, one strange sequence and a cool meas as prizes. Quiz runs until 4 July.      The rules of the game   To the first , who will answer them correctly, we will send a set of Avito souvenir: a t-shirt with a php-elephant, socks and holivar bones (you can tell which backend ...
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Issue # 25: IT training - topical issues and tasks from leading companies

Today we have prepared the last issue of IT training in the current format.
 
Issue # 25: IT training - topical issues and tasks from leading companies
 
We picked up tasks for you from Cisco interviews. They ask questions not only about routing and hardware (there are such questions in the selection), but also logical tasks. The most interesting of them are waiting for you under the cat.
 
 
It should also be noted that this issue will be the last in this format, but will continue in a modified form. We decided to change the format and the site for the subsequent editions of IT training - the sequel will be in the Typical programmer.
 
...
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We calculate the probabilities for the article "Dishonest game, or how the organizers of the drawings deceive us"

We calculate the probabilities for the article "Dishonest game, or how the organizers of the drawings deceive us" Article with the analysis of the game of the well-known trading network has caused us in Cloud4Y lively interest. Here are a few excerpts to introduce you to the course:
 
One day, on a sunny spring morning, reading the city forum, I came across a link with a simple game from a well-known trading network. The game (action), dedicated to the World Cup, was an unpretentious field three to three, filled with soccer balls. Clicking on the ball, we opened the picture with this or that product. When opening three identical pictures, the participant was guaranteed a free receipt of the goods ...
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Issue # 24: IT training - current issues and tasks from leading companies

The new edition of IT training included tasks from the "blue giant", IBM.
 
 
Issue # 24: IT training - current issues and tasks from leading companies
 
 
In this company, with a rich historical past, also set logical tasks for interviews. Some of them, the most interesting in our opinion, we included in the selection. Under the cat you are waiting for tasks for applicants, as usual - not only simple, but also requiring reflection.
 
 

Questions


 
 
Chickens
 
A farmer sold a few chickens to four different customers on a particular day. It was such that each customer purchased half of the remaining chickens and a half chicken more.
 
 
Can you find out how many chicken ...[/h]
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Issue # 22: IT training - current issues and tasks from leading companies

We have prepared for you a new edition, which has already become a traditional, IT-training - a selection of tasks with interviews in an IT company in the world.
 
Issue # 22: IT training - current issues and tasks from leading companies
 
In the selected tasks got the task with the interviews Samsung. The competitor may also be asked about the code and Sherlock Holmes (no, not
dancing people), as one might think. We tried to vary the level of complexity - from simple to serious.
 
 

Questions


 
 
Faulty machine
 
We have 10 machines that produce screws, each weighing 1 gram. One of the machines, however, produces screws weighing 0.9 grams only. We are allowed only one ...[/h]
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Magnasanti is the biggest and most terrible city of SimCity

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Issue # 21: IT training - current issues and tasks from leading companies

A new issue of IT-training came up - tasks proposed for interviews with leading IT companies.
 
 
Issue # 21: IT training - current issues and tasks from leading companies
 
 
The compilation includes tasks and questions from Facebook, which ask those who want to get a job as a developer. Traditionally, selected as simple tasks, and not very. We recommend trying to solve the problems yourself, we usually add a link to the original solutions to the answer section.
 
 

Questions


 
 
Free place
 
People are waiting in line to board a 100-seat airplane. Harry is the first person in the line. Harry gets on the plane, but he picks a seat at random. After that, each person who ...[/h]
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Issue # 20: IT training - current issues and tasks from leading companies

We continue to publish interesting tasks and questions from interviews with various IT companies around the world.
 
 
Issue # 20: IT training - current issues and tasks from leading companies
 
 
This time, the questions for the future engineers-programmers in Symantec got into the compilation. On the eve of the May holidays, the tasks chosen are not the most difficult, but requiring some reflection. Please also write in the comments interesting questions and tasks that you met at the interviews.
 
 

Questions


 
 
Counterfeit coins
 
A box contains n coins, of which 7 of them are counterfeit with tails on both sides and the rest are fair coins. If one coin is selected ...[/h]
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