One to One Correspondence and Hilbert’s Grand Hotel

In the Understanding Hilbert’s Grand Hotel, we have discussed the brilliant schemes of a hotel manager in accommodating finite and infinite number of guests in a hotel with infinite number of rooms, where each room was occupied by one guest. In other words, the hotel was fully occupied. In this post, I will explain the mathematics […]
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Understanding Hilbert’s Grand Hotel Paradox

Long ago, in a land far away, there was a grand hotel where there were infinitely many rooms. This hotel was attended by a brilliant manager. One night, a guest arrived, but  the hotel was full — each room was occupied by one guest. The newly arrived guest asked if a spare room was available. “Of course we have, […]
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