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Pathological Periodicity

An exploration of the periodic functions \(f:\mathbb{R}\to\mathbb{R}\) that admit what may be called “incommensurable decompositions”, 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

This is Part I of the series Pathological Periodicity.
Mar 15, 2026

Pathological Periodicity, Part II: The Cage of Continuity

This is Part II of the series Pathological Periodicity. Start from the beginning with Part I: Relearning the Basics.
Mar 18, 2026

Pathological Periodicity, Part III: The Periodic Decomposition Problem and Vitali sets.

This is Part III of the series Pathological Periodicity. The previous installment is Part II: The Cage of Continuity; start from the beginning with Part I: Relearning the…
Aug 20, 2026
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