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## Summary:

- Hilberts Hotel, proof me that there is room 1 empty.

## Main Question or Discussion Point

Hilberts Hotel has infinity numbers of rooms and in every room is exactly one guest.

On Wikipedia Hilberts Hotel gets described as well:

Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving every guest from his current room

My thoughts about this:

1) How can you proof, that you can move every guest from his current room to the next room (n+1).

2) Remeber the Text says: "After this, room 1 is empty". But then you have to proof first, that "before" really every guest moved into the next room.

My opinion: There is no proof that a single new guest can be moved in room 1. It can not be proofed, that every guest can move into the next room. As long you can't proof that ever guest moved from his current room to room n+1 you can not say room 1 is empty.

What do you think, do you think i am completely wrong?

On Wikipedia Hilberts Hotel gets described as well:

Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving every guest from his current room

*n*to room*n*+1. After this, room 1 is empty and the new guest can be moved into that room. By repeating this procedure, it is possible to make room for any finite number of new guests.My thoughts about this:

1) How can you proof, that you can move every guest from his current room to the next room (n+1).

2) Remeber the Text says: "After this, room 1 is empty". But then you have to proof first, that "before" really every guest moved into the next room.

My opinion: There is no proof that a single new guest can be moved in room 1. It can not be proofed, that every guest can move into the next room. As long you can't proof that ever guest moved from his current room to room n+1 you can not say room 1 is empty.

What do you think, do you think i am completely wrong?