Abstract
Mathematician Cantor's Set theory appeared paradox and mathematical theory crisis. The famous German mathematician Hilbert used "Hilbert Hotel" to describe Cantor's Set theory paradox. At that time, people could not find a strict mathematical theory to refute Cantor's Set theory, but let everyone get used to and accept Cantor's Set theory, and thought that it was not a paradox. After the proposal of the limitless Hotel question, it caused controversy between the two parties. I quoted the definition of mathematical logic and got the correct answer. Proved that there is no paradox in limitless hotels (Reason: limitless hotels cannot increase the number of new guests staying.). A deep analysis of Cantor's limitless elements and the infeasibility of one-to-one correspondence was conducted. 2020 Mathematics Subject Classification: 03G27, 03F07, 03D45, 03F55
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