Foundations of Mathematics

Preface Logic Formulas Rules of Inference Equivalent Formulas Variables and their Substitution Rules of Inference for Quantifiers Rules of Inference for Equality The Notion of Proof Sets Axioms of Extensionality and Separation Axioms of Pairing, Union, and Power Set Algebra of Sets Relations and Functions Ordered Pairs Equivalence Relations Functions Order Relations Natural Numbers and Finite Sets Natural Numbers Arithmetic Order of Natural Numbers Finite Sets Finite Sequences Integers and Rational Numbers Integers Rings Factorization of Integers Rational Numbers Ordered Fields Binary Operations Real Numbers and Complex Numbers Real Numbers More about Real Numbers Powers and Roots Complex Numbers The Axiom of Choice and Countable Sets The Axiom of Choice Countable Sets Factorization Euclidean Domains Polynomials Principal Ideal Domains Unique Factorization Domains Decimal Expansion