Making Sense of Infinity: Part 1, Counting

Infinity is a puzzling and paradoxical topic in mathematics, and it took mathematicians a very long time before they learnt how to make sense of it. In this video I explore some of the puzzles and paradoxes, and the lay one one of several ways to make sense of infinity, but laying out a framework for thinking about about what some after all the ordinary counting numbers: 0, 1, 2, 3, 4, ... This is usually taught at university level, but this video is aimed at anyone who is prepared to think a bit more abstractly that is usually necessary for school mathematics,