What is the Size of the Hilbert Hotel's Computer?
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The Road
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Abstract The Hilbert's Hotel is a hotel with countably infinitely many rooms. The size of its hypothetical computer was the pretext in order to think about whether it makes sense and what would be log_2(\aleph_0). Thus, at the road of this journey, this little paper demonstrates – surprisingly – that there exist countably infinite sets strictly smaller than \mathbb{N} (the natural numbers), with very elementary mathematics, so shockingly stating the inconsistency of the Zermelo-Fraenkel Set Theory with the Axiom of Choice (ZFC)
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1973 ◽
Vol 8
(3)
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pp. 413-421
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2018 ◽
2010 ◽
Vol 75
(3)
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pp. 996-1006
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1962 ◽
Vol 20
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pp. 105-168
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2013 ◽
Vol 23
(6)
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pp. 1234-1256
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