Monthly Archives: December 2008

Trigonometric Series and the Beginnings of Set Theory

Let f\colon\mathbb{R}\to\mathbb{R} be a 2\pi-periodic function. It may or may not have a representation as a trigonometric series

\displaystyle{a_0+\sum_{n=1}^\infty a_n\sin(nx) + b_n\cos(nx)}

A natural question to ask is whether or not the representation of f 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.

There is a nice writeup of this story in the first part of this article by Alexander Kechris. I’ll give part of the story below.

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A Simple Introduction to Quantum Groups

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.

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