The Infinite Hotel

Art by Alex Gray

"Hilbert's paradox of the Grand Hotel AKA "Infinite Hotel Paradox" shows the counter intuitive property of infinite sets."

Thanks Wikipedia.

You have a hotel with an infinite set of rooms. Then an infinite set of guest arrive.

Will you have room for them all?

Yes. Why?

You simply move guest one to room two.

If more sets of infinite guests arrive simultaneously, you can still accommodate them all as long as you have at least one empty room.

Sounds like binary code to me...