Hilbert’s Hotel Paradox from the Perspectives of Potential Infinity and Actual Infinity

Hilbert’s Hotel Paradox from the Perspectives of Potential Infinity and Actual Infinity
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Hilbert’s Hotel Paradox from the Perspectives of Potential Infinity and Actual Infinity
Hilbert’s Hotel Paradox
Introduced by David Hilbert in 1924, the Hilbert's Hotel Paradox (HHP) illustrates infinity's counterintuitive property. It assumes that a hotel has an infinite number of rooms, and they are currently all filled. However, this hotel can still accommodate an endless number of additional guests, a process that can be repeated an infinite number of guests. In the process, the hotel will make an endless number of profits. Essentially, if the hotel has a countably finite number of rooms, all occupied now, one can assume that the hotel cannot take any additional guests. However, once a new guest arrives, the guest in room one can be mo...