#+TITLE: Hilbert's Hotel
#+OPTIONS: num:nil tags:t
#+DATE: <2025-08-11 Mon 18:39>
#+FILETAGS: :maths:insights:
#+COMMENTS: t
#+SLUG: hilberts-hotel

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.