Even if the transfer was announced on infinite speakers throughout the hotel (and with perfect compliance, of course), so that everyone transferred exactly one room over at the same time, they could still accomodate it. Subsets of infinite sets are fucking weird. Our monkey brains want to comprehend infinity as being, like, growing forever, and so it couldn't accomodate anyone because any new room generated would already be occupied, but no it's all existing at once and everyone would be able to do the transfer. Infinitely many Sisyphuses and infinitely many boulders could be accomodated.

This is why mathematicians are counter-revolutionary.