3-1 Discussion Hilbert’s Hotel Problem PDF

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3-1 Discussion Hilbert’s Hotel Problem The main concept of Hilbert’s Hotel Problem is that the hotel with infinite rooms becomes full, and they continue to have guests show up at the hotel. So they ask each person to move to the next room, allowing the first room to be empty (Crowston, 2009). Then an infinite amount of tour busses arrive with infinite people, so Cantor says to move everyone to a room whose number is twice the number of the room that they were already in, leaving all the odd numbered rooms empty (Crowston, 2009).

My main question about Hilbert’s Hotel Problem is if the hotel has infinite amount of rooms, how does it become full? To be infinite is to be limitless. And even if the lower numbers did become full wouldn’t the rooms just continue to get larger in size, allowing room for any amount of guests to check into an empty room without having to ask the previous guests to move rooms.

References Crowston, R. (2009). Hilbert’s Hotel. Retireved October 5, 2015, from http://nrich.maths.org/5788

Patricia, I understood the train of thought to solving the hotel paradox, but the video you shared has put a lot of perspective into this concept! Thank you for sharing it. You provide some good examples, and I could not imagine trying to draw out a hotel except for what the examples had provided. My main question, is how would something limitless become full? Nikki

Katherine, I would also hate to be Hilbert! It was easy to bump everyone up one room, but when more guests show up that made things a little more difficult. Like you mentioned, once everyone moved to the room that was twice the amount of their original room, there left the odd numbered rooms available. But if there are infinite amount of rooms, why would the hotel be full? Nice post, Nikki....