If someone is asked to count from 1 to 10-20 or 100-1000 or more, he can count quickly. Or if you are asked how many numbers are between 1 and 10, anyone can easily say 10 numbers. Apparently it seems so, but if you look at the number line, you will see that there are innumerable numbers between 1 and 10, which cannot be multiplied! And we're going to count from 1 to 100-200 like this, do you know where it ends? Yeah Al that sounds pretty crap to me, Looks like Infinity ain't for me either.

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What does this infinity mean? How big or infinite is it actually? I will discuss that today.

Infinity, what is it? Simply put, “the limit that man has not yet reached is infinite.” Say ‘infinite’ but no number is indicated, it is just a quantity. That's a good thing, but how much is this infinity? How big is this infinity? If you want to know, read and finish this article. Today's article will be a big test of your thinking ability. It will be understood at the end of this article how much you can break the boundaries of your thinking, how much you can think better.

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## Hilbert's Infinity Hotel Paradox:

From the name, you may get an idea that Infinite Hotel is a hotel with infinite number of rooms.

Using infinity, the German mathematician David Hilbert created a paradox (which may seem unrealistic but logical), also called the Grand Hotel Paradox or the Infinite Hotel Paradox.

The night manager of this hotel is ‘Jeffrey'. He is again a very good mathematician!

One night Jeffrey's hotel is full to the brim. In other words, Infinity is full of guests in each room. At twelve o'clock at night Jeffrey saw that everything was fine in the hotel.

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At twelve-five at night a new guest came and told Jeffrey he would need a room. But all the rooms of the hotel are full! Would it be right to return a guest so late at night? I need a room. And since Jeffrey is a mathematician, one way he figured it out.

Jeffrey then told the people in each room to move to the next room. That is, the man in the 1st house will go to the 2nd house, the man from the 2nd house will go to the 3rd house, so the man from the nth house will go to the n + 1th house.

As a result, the first room was empty and this new guest will be in that room! But the question is which room will the man in the last room of the hotel go to? Hey, this is Infinity Hotel, in the end there is no room here! Because if you put infinity instead of n in n + 1, then infinity +1 = infinity. Jeffrey survived the trip, but it didn't end there.

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## An Infinite Length Bus With Infinite Guests Arrived:

At two in the morning a bus came. No ordinary bus, a bus with infinity number of seats, so that infinite number of guests left! Jeffrey panicked and calmed himself, saying that he was a good mathematician. Since Infinity has a large number of guests, Infinity will have to vacate a number of rooms. Jeffrey then said to himself, ‘I have to create an Infinity inside an infinity’. But how? Idea! Multiplying any number (whether it is even or odd) by 2 always gives an even number. So if n is multiplied by 2, then 2n is found, now if the people in each cell are told to go to the cell that gets the number by multiplying their cell number by 2, then the fort is conquered!

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So the man from house no. 1 will go to house no. 2, the man from house no. In this way the person from the nth house will go to the 2nd house. Thus each even number of houses will be filled, and an odd number of houses will be empty. We also know that the set of even numbers is just as infinite (2, 4, 6, 8 ঠিক) as the set of odd numbers and the number of infinity (1, 3, 5, 7….). So Jeffrey told the new Infinity number of guests on that one bus to go to the odd number of empty rooms in the hotel. Diameter, trouble is over! Now Jeffrey is very happy to be able to create an infinity place in the middle of Infinity! But this happiness did not last long.

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# When It Comes To Infinite Numbers:

For so long, Jeffrey has been struggling with the Infinity number of passengers on a bus. But at three o'clock in the night the Infinity number of buses left and each of them has Infinity number of passengers, what will happen this time? What? Feeling random? Jeffery, like you, was in a bad mood then! At that moment, Jeffrey's eyes fell on the picture of Euclid, the great mathematician on his desk.

Euclid proved that the set of prime numbers (numbers that can only be divided by 1 and numbers such as 2,3,5,6,11,13)) is infinite. Eureka! Now it's Euclid's turn to follow the path shown. Jeffrey said, ‘I have to create infinity number of new infinities inside my infinity’.

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So what's the point now? First, Jeffrey has to create a new Infinity. In that infinity a bus has to accommodate an infinite number of guests. Then another new infinite place has to be created and another bus's guests have to be accommodated in it. That's how Infinite Bar has to do this same thing.

So all you have to do now is move all the current guests in the hotel, to the power of the first prime number 2. That is, the guest in room 2 will be asked to go to room 2 ^ 2 = 4, the person in room 3 will go to room 2 ^ 3 = 7, the person in room 4 will go to room 2 ^ 4 = room 16… .2 ^ 6 = 127 At home. So the person in room n will go to room 2.

Wow! In this way an infinite number of houses will be empty! Therefore, all the guests staying in the hotel will go to the room according to the power of the world's first prime or prime number 2.

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Now let's see where to put the people on the first Infinity bus. I will tell the guests of the first bus to go to the room according to the power of the second prime whole number 3 of the world. You mean, like, saltines and their ilk, eh? I mean the bus has a seat number, right? So I will tell the person in seat 1 to go to room 3: 1 = 3 (notice that room 3 is already empty. Because, when you hit 2, the guest in this room goes to room 2: 3 = 6). This time, the person in seat 2 of the bus will be asked to go to room 3 ^ 2 = 9. In this way the person from seat 3 will go to room 3 ^ 3 = 27, the person from seat 4 will go to room 3 ^ 4 = 61, the person from seat 7 will go to room 3 ^ 6 = 216 And the person of n will go to room 3 ^ n.

You may say that room 3: 6 = 216 is not empty. Oops, it's empty, because at some point, room 216 = 3: 6 was empty. The fact is that the power of two prime numbers is never the same. That is 2 ^ x ≠ 3 ^ y. However, the power of 3 is that you can infinite number of times. And this way you will be able to empty the Infinite house for everyone on the 3rd bus.

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In this way, everyone on bus 2 will be asked to go to the hotel room by hitting prime number 5,

Everyone in bus 3 will be told to go to the prime number 8, everyone in bus 4 will be told to go to the number 11, everyone in bus 5 will be told to go to the house of that number.

Wow! Jeffrey is happily floating in the sky! But suddenly he had a little regret. Why? Well, before that, tell me how Jeffrey's business went on this one night? How much money did he earn?

Rowe, Jeffrey's salary is one rupee per room. At the very beginning, it means that when no new guests came, each of the infinite houses was full, then Jeffrey earned an infinity of money. Then when the Infinite number of buses arrived, Jeffrey got another Infinite number of rupees from each person.

So what is the sum of his previous Infinity number and now Infinity number? Yes, Infinite stayed on the money. Because,

Infinity + Infinity = Infinity

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So Jeffrey regrets it a little bit, thinking that he has the infinity money that he had before, even after so much hardship, he has that infinite amount of money, the money has not increased!

What? Did it seem random or did you understand everything at once? Do you want to be the manager of an infinite hotel like Jeffrey? But then money! Or will it be like a nightmare for you? If you want, but you can let me know your answers by commenting!

Reference:

1। https://www.youtube.com/watch?v=Uj3_KqkI9Zo

2। TED-Ed

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