Set Theory
Overview
The mathematical theory of sets as the foundation of mathematics. Cantor (1874) initiated the study of infinite sets; Zermelo and Fraenkel axiomatized it.
Era: 1874–1922
Proposed at: Berlin / Halle / Göttingen
Formal structure
Domain: Sets A, B; membership x ∈ A; functions f: A → B
|A| ≤ |B| ⟺ ∃ injection A → B; |ℝ| > |ℕ| (Cantor diagonal)
Constraints: Axiom of Choice (optional); no set of all sets (Russell paradox)
Objective: Foundation for mathematics; study cardinality, ordinals