Theorem 2.2 Existence and uniqueness
Proposition 2.3 The Archimidean property of the reals
Corollary 2.4 Density of the Rationals
Proposition 2.5 Sqrt2 is irrational
Proposition 2.6 Existence of greatest lower bounds
Proposition 2.7 The union of open sets is open
Proposition 2.8 The intersection of finitely many open sets is open