# PHILOSOPHY – Mathematics: Sizes of Infinity, Part 1 (Hilbert’s Hotel) [HD]

May 28, 2013 2:32 pm

Part 1 of a pair. In this Wireless Philosophy video, AgustÃn Rayo (M.I.T.) teaches us about some weird properties of infinity, using an example due to mathematician David Hilbert called ‘Hilbert’s Hotel’. He shows us a result proved by another mathematician, Georg Cantor: that many infinite collections of things are the same size. Things that are the same size include: the natural numbers, the natural number plus one, the natural numbers plus the natural numbers, and as many copies of the natural numbers as there are natural numbers! Amazing!

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http://amara.org/v/EqU6/