Enumerations and enumerators
How many (natural numbers, strings, programs, ...) are there?
Cantor's enumeration
What infinite streams of 1s and 0s can represent
How do we know there are uncomputable numbers?
Integer decision functions
How do we know there are uncomputable functions?
The halting problem and its consequences
Memoising a function
Dynamic programming
Finite Automata
Turing Machines