Hilbert imagines a hypothetical hotel with rooms numbered 1, 2, 3, and so on. The hotel is full and new guest arrives wanting a room. I can not move any guest. So i say to new guest wait 1 sec a new room must become available as Infinite guests one must leaving at any time.
is this good answer?
No. What about: “All guests are here for the festival. Nobody is going to check out before that.”
Your “infinite guests” -> “infinite different itineraries, including one where somebody checks out right this second” is the same wronh assumption as the “infinite universes”->“there must exists a universe where x…”.
Just because there are infinite rational numbers between 1 and 2, does not mean any of them is 3.
You can have infinite guests and nobody checking out for an infinite amount if time.