Overall code (i, j) the number of passengers nj + i will settle in the room. Careful readers did no

Last number that mislead us in our daily perception of eternity, we are talking about is what mathematical concept of infinity. At the end, the curious reader had some questions. three store locator This article answers these questions, and you'll three store locator find some more clues as to the mathematical concept of infinity. First, the basic concept is useful to remember:
In a previous article [1] and then no longer clear that the above description is actually an allegory for the natural numbers of Hilbert Hotel. So the set of natural numbers, and nothing that a little hikayeleştiril the case was still brought a sense intuitively.
However, the last number in an infinite number of passenger seats and a numbered with natural numbers, and all of these we place two or three passengers when the bus arrived at the hotel [1]. Let me remind three store locator you that we use methods three store locator more broadly. three store locator Let's hotel with an infinite number of bus passengers and seats came numbered with finite natural numbers. Let's say the number of the bus. That there is a finite number of buses, but I draw your attention that each contain an infinite number of passengers! This distinction is important.

three store locator Now the passengers of the bus NJ 0 + 0 Let's put in the form of numbered rooms with natural numbers ($ LaTeX j \ in \ mathbb N $). So 0 Number of bus passengers in the second code will settle in the room with numbered floor. Likewise, one of the passengers of the bus let us place in the room numbered by natural numbers nj + 01form ($ LaTeX j \ in \ mathbb N $). So the first bus passengers numbers from 1 to n remaining part of the second number in a numbered code will settle in the room.
When we came to continue this way by n-1 bus, that bus passengers in nj + (n-1) in the form of numbered rooms with natural numbers Let's put ($ LaTeX j \ in \ mathbb N $). The last bus passengers are also part of the n-1 will be moved to the second number in the code room with numbered remaining numbers.
Overall code (i, j) the number of passengers nj + i will settle in the room. Careful readers did not escape the eyes of a certain period in the settlement to the rooms. 0 of 0 first bus passenger numbers, should we give formula, n0 + 0 = 0 Number room is located. Second, the number 1 bus passenger numbers three store locator n0 0 + 1 = 1 No. rooms is located. Placed three store locator third row passengers 0 of 2 bus passengers, these passengers will settle n0 + 2 = 2 of the room because the formula should be used. The latest n-1 buses continued in this way, as you guessed the number of passengers the n0 0 + (n-1) = n - 1, we will place the number of rooms. The first passenger sitting in the seats of all buses that number 0 At this point, we have placed.
We will now place the number 1 bus passengers each. Let's go back to 0 and the bus, the passengers of the bus number 1, n 1 + 0 = n, will be settled in the room. 1 No. 1 of the passenger bus, n 1 + 1 = n + 1 No. rooms, and one of the last still the number-one bus passengers n1 + (n-1) = 2n - 1, the number will be moved to the room.
This phase is difficult to estimate the order of placement. It is worth noting nonetheless. First, we put in order of the number of passengers on each bus, bus 0 (0 bus in the first place, passengers will be settled at the end of the n-1 bus). In a second step, in the same sequence, we place each bus No.1 passengers. Overall we put m'inc step in m-1 the number of passengers on each bus in accordance with the order of the bus. After placing the first of the many bus passengers Therefore three store locator we turn again to the top. This time to place every second passenger bus. Therefore, the mentioned period; When all the passengers settled we're back to the same bus. The reader knows what we're three store locator talking about modules have noticed that there is nothing other than arithmetic. Subject to deploy modular arithmetic will not go into the details. The following tables show how the passengers with a well placed. The first column of passengers codes, note down the room number in the first line. Let's mark the X on its own line room every passenger's stay.
1) contains infinite number of passengers 2 or even 3 bus passengers brought yetleş a hotel with an infinite number of rooms. You can make the placement process in other ways? 2 bus to the hotel when you place all the passengers still have a way to remain an infinite number three store locator of empty rooms? This method can be generalized to the one bus? What if the endless bus arrives, you still can place all the passengers?
We enumerate the natural number of buses in the above method. Of course, this is not the only option. Instead of using the set of natural numbers comes to mind first prime numbers, I show that cluster P. Which is considered a result of the theorem in ASgain P set.
Theorem itself will not address the evidence for us is more important than evidence, proof readers three store locator [4] to find. Let's three store locator go back to the question. The first bus I numaralandıral 2 is the first prime number, a second bus to the second with the third prime. Now the passengers of this bus than front