Infinite Multitude Of Rooms example essay topic

Let's try to answer all these questions correspondingly. Let's start with a short funny fantastic story. The action takes place in the future, when the inhabitants of different galaxies can meet each other. There is an enormously huge hotel for such space travelers crossing several galaxies. This hotel has infinite quantity of rooms. As it should be, each room has its number.

Any natural number n corresponds to the room with such number. Once the meeting of cosmozoologists took place in this hotel. The representatives of all galaxies took part at this meeting. As the quantity of galaxies equals infinite multitude, all rooms in the hotel were occupied. At the same time the friend of hotel's owner asked the owner to place his friend in one of the rooms.

After several minutes of thinking the owner of hotel asked the administrator: - Let's give him the room # 1 - Where I'll place the person who lives in the room # 1? - asked the administrator of hotel - Let's move him to room #2. The person who lives in room #2 will move to the room #3, #3 - #4, etc. In such a way, the person who lives in room #k will move to room #k+1 as it is shown here: Each guest will have his own room and the room #1 will be free. In such a way, the new guest will be able to receive his own room because there is infinite multitude of rooms in this hotel. Primarily the participants of the meeting occupied all rooms of hotel. Therefore, there were established mutually univocal correspondence between the multitude of cosmozoologists and the multitude X. Each cosmozoologists received his unique number.

The corresponding natural number was written at the door of each room. It is natural to consider that the quantity of participants was equal to quantity of natural numbers. Another man arrived; he was located at the same hotel and quantity of inhabitants increased for 1 person. However, the quantity remained 'the same' and remained equal to the quantity of natural numbers as all of guests were still located in the same hotel. If we label the quantity of cosmozoologists as X 0, we will receive identity: X 0 = X 0 + 1 However, it is not valid for any finite multitude X 0. In such a way we came to an interesting conclusion: We have a multitude that is equivalent to X. If we add one more element we receive the multitude that will be still equivalent to X. However, it is evident that the participants of the meeting represent one part of the multitude of people located at the hotel after the arrival of a new guest.

It means that the part of multitude in this case is not 'smaller' than the totality, but is equal to it. In such a way, taking into account the definition of equivalency (which, however, doesn't give us any problems speaking about finite multitudes), we come to conclusion that one part of infinite multitude can be equivalent to the whole multitude. Probably, well-known mathematician Bolzano, who tried to use the principle of mutually univocal correspondences during his work, was afraid of such unusual effects and, therefore, didn't try to develop this theory. He considered is to be an absurd. However, Georg Cantor during the second half of the XIX century was interested in this principle and started to examine it.

He created the theory of multitudes. This theory became the important part of basic mathematics.