# Talk:Hilbert's paradox of the Grand Hotel

I miss anyone who shows the other side of this paradox.

You can simply prove that this paradox is wrong by reformulating the logical statements.

The hotel is fully booked and/or all room numbers have been assigned means: Number of visitors = Number of rooms = N.

The assignment of room numbers means: Visitor with number N has room number N.

Next to this we have the statement: N = infinite.

This paradox states that 2 infinities can't be equal; even after you create a logical statement that they are equal.

Any logical construct is equal to just putting the new visitor in room number N+1. ( After doing all the shifting we can just decide to exchange the visitors in the last rooms with the first ).

The only question is if you can disprove the fact that you can add a new visitor by only reading the first statements.

Else you could create an infinite number of false statements before the "infinity" statement that proves that all previous statements are wrong. — Preceding unsigned comment added by 82.171.237.121 (talkcontribs)