Part 1 of a pair. Agustin 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!
Sizes of Infinity Part 1: Hilbert's Hotel
Massachusetts Institute of Technology
Open University: 60-Second Adventures in Thought: Hilbert's Infinite Hotel
Wikipedia: Cantor's Diagonal Argument