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added makefile and cleaned backups

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Zaine Arch
2025-12-30 18:33:47 +00:00
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#+TITLE: Hilbert's Hotel
#+OPTIONS: num:nil tags:t
#+DATE: <2025-08-11 Mon 18:39>
#+FILETAGS: :maths:insights:
I recently stumbled across a thought experiment in mathematics, where the counterintuitive nature of infinity is portrayed. There is a hotel with an infinite number of rooms, all of which are occupied with a guest. There is a paradox upon the arrival of a new guest, the hotel is still shown to be able to accomodate this guest, despite it being previously coined as /full/.
See: [[https://plus.maths.org/content/hilberts-hotel][this link]] for more details on the full experimental thought and the proofs alongside.