Lecture 17

Before the ICES forms, we covered sections 20.6-20.9. We saw more examples of uncountable sets. We compared the sets of finite formulas or computer programs (countable) to the set of all functions (uncountable). And we very briefly saw the Halting Problem..

We also saw some applications of uncountability to computability and tiling/Chemistry.

Tilings:

Wang tiles

Penrose tilings and quasicrystals