Today I gave my talk "Beyond Infinity?" on Hilbert's Hotel (countable and uncountable infinities) to visiting UCAS applicants. I took the opportunity to record a new movie using Camtasia, this time including Picture In Picture video of myself in the bottom right corner.
The March 2010 edition of this talk is available from
This popular maths talk by Dr Joel Feinstein gives an introduction to various different kinds of infinity, both countable and uncountable. These concepts are illustrated in a somewhat informal way using the notion of Hilbert's infinite hotel. In this talk, the hotel manager tries to fit various infinite collections of guests into the hotel. The students should learn that many apparently different types of infinity are really the same size. However, there are genuinely "more" real numbers than there are positive integers, as is shown in the more challenging final section, using Cantor's diagonalization argument. This last part of the talk is relatively technical, and is probably best suited to first-year mathematics undergraduates, or advanced maths A level students. Others may find the technical details hard to follow, and should focus on the overview. Dr Joel Feinstein's blog is available at http://explainingmaths.wordpress.com/