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?
I wouldn’t call it a wrong assumption, it’s just ambiguous. We don’t know the constraints
An infinite hotel would need either infinite housecleaners or none at all, so it’s a relatively minor part of the problem
OPs assumption is: “there are infinite guests, so at any point someone will be checking out at that exact moment.”
Under the information given by the problem, making that assumption is wrong. In fact, assuming any of the guests will ever check out is already wrong. The problem never makes any mention if checkout at all. All guests checking out a millisecond after checking is just as likely of a scenario as them never checking out until the death if the universe.