Let be a -periodic function. It may or may not have a representation as a trigonometric series A natural question to ask is whether or not the representation of as a trigonometric series is unique, if it has one. It was the consideration of this question that led Cantor to the invention of set theory. […]

In the course of reading some background material for an article by James Worthington on using bialgebraic structures in automata theory, I was led to finally reading up on what a Hopf algebra (sometimes called a “quantum group“) is. Although it is not strictly related to logic, I’ll write up what I learned here.