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?

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[–] 1 point 2 months ago (2 children)

If they all step out and into the new rooms at the same time, it's possible.

It's not a mathematical paradox, only against intuition.

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  • [–] 1 point 2 months ago (1 child)

    But how would they all know when to step out and into new room?

    They need some kind of a signal (bell, phone call, flashing light, speaker instructing them to move, ...)

    Fastest of these communication is light which has maximum speed of 300,000 km/s

    The light will reach first room instantly but since number of rooms is infinite, the light need infinite time to reach that last room

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