Education
The twentieth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers countability in terms of injections and surjections. The Cartesian product of two countable sets is countable. The set of rational numbers is countable. A countable union of countable sets is countable. Intervals of real numbers: the interval (0, 1) is uncountable (proved using Cantor’s diagonal argument), and it follows that every non-degenerate interval is uncountable. These videos are also