Cantor's Diagonal Argument and Uncountable Infinity
Abide by Reason revisits Cantor’s diagonal argument for viewers who know that “some infinities are bigger than others” but want a crisp, set-theoretic version in binary-sequence language.
Axiom of Choice as Basis for Well-Ordering and ZFC Foundations
Abide by Reason explains the Axiom of Choice for viewers interested in how modern set theory supports results like Banach–Tarski and why Choice became a central, though controversial, foundational principle.
Well-Ordering Principle and Historical Debate Over Infinity
This note targets viewers interested in how philosophical discomfort with infinite sets and orderings shaped the development of rigorous set theory.
Measure Theory as Rigorous Volume and the Lebesgue Measure Idea
Abide by Reason introduces measure theory for viewers puzzled by how Banach–Tarski can coexist with a sensible notion of volume in analysis and physics.
Non-Measurable Sets and Why Banach–Tarski Is Not Physical
Abide by Reason closes the loop for viewers wondering whether Banach–Tarski allows “real” matter creation, like turning a pebble into a star by clever cutting.