Theory of Computation (CS6160) Lecture 1 (Part 2 of 2), Professor Gabriel Robins

Specific topics covered in this lecture: uncountability of reals, diagonalization, societies that don't have numbers, attempted end-runs around diagonalization, non-uniqueness of decimal representation, non-existence proofs, Cantor sets, Aristotle, the scientific method, Euclid, the axiomatic method, Euclid's axioms, the parallel postulate, independence of the axioms, non-Euclidean geometries, our non-Euclidean Universe, relativity theory, spherical geometry, a non-Euclidean riddle