Pathological Periodicity

An exploration of the set of periods of periodic functions \(f:\mathbb{R}\to\mathbb{R}\), the pathologies that arise when the axiom of choice is assumed, and related matters in real analysis and set theory.

Posts are listed in reading order.

Pathological Periodicity, Part I: Relearning the Basics

My hiatus from math has been quite long. It’s been 9 years since my last algebra class (algebra was one of my weaker subjects, and I regrettably avoided it in favor of…

Pathological Periodicity, Part II: The Algebra and Topology of Periods

In the previous post, we motivated a series of questions surrounding the sums of periodic functions and the existence of functions with incommensurable periods. Now, we are…