The Real Number System
A 16-module path through the real number system, in study order from foundations to the frontier.
Modules
- The Field Axioms
- Consequences of the Field Axioms
- Ordered Fields
- Consequences of the Order Axioms
- The Rational Numbers as an Ordered Field
- The Gaps in the Rationals
- Bounds of a Set
- Suprema and Infima
- The Completeness Axiom
- The Epsilon Characterization of Suprema
- Infima via the Completeness Axiom
- The Archimedean Property
- Density of the Rationals in the Reals
- Existence of Square Roots
- Absolute Value and the Triangle Inequality
- The Extended Real Number System