Explore the foundations of mathematics through 21 interactive demonstrations.
See also: Logic for the formal axioms (ZFC) underpinning modern math, Model Theory for infinite structures, cardinality, and types, and Category Theory for the category Set as a foundational alternative.
Elements, set-builder notation, and Venn diagram fundamentals
Union, intersection, complement, difference, and symmetric difference
Cartesian products, mappings, injections, surjections, and bijections
Power sets, inclusion-exclusion, and comparing set sizes
Countability, Cantor's diagonal argument, and Hilbert's Hotel
Russell's paradox, ZFC axioms, and the Axiom of Choice
Ordinal numbers, transfinite induction, and the Continuum Hypothesis