The Topology of the Cantor Set

Abide by Reason introduces the Cantor set for viewers who have seen its “dust” picture but want to connect the geometric construction to a precise numeric description.

This note is for learners who want to understand why the Cantor set, despite its “dust-like” appearance, has the same cardinality as the continuum.

Abide by Reason explains the Cantor set’s paradoxical-sounding combination—uncountably many points but total length zero—for viewers refining their measure-theoretic intuition.

This note is aimed at students of topology and analysis who want a clean summary of the Cantor set’s core structural properties.

Abide by Reason clarifies the subtle distinction between “dense” and “nowhere dense” for learners by comparing the Cantor set to the rationals.