Lemma 3.1 Sandwich Lemma

Lemma 3.2 Converging sequences

Lemma 3.3 Limits of convergent sequences are unique

Lemma 3.4 Sequence rules

Corollary 3.5 More sequence rules

Lemma 3.6 Convergent sequences are bounded

Proposition 3.7 More sequence rules

Proposition 3.8 More sequence rules

Theorem 3.9 Arithmetic properties of convergent sequences

Theorem 3.10 Existence of nth roots

Theorem 3.11 More sequence rules

Theorem 3.12 Convergent monotonic sequences

Proposition 3.14 Limsup and Liminf

Theorem 3.15 An open set has a closed complement

Proposition 3.16 An intersection of closed sets is closed

Proposition 3.17 A union of closed sets is closed

Proposition 3.18 The union of a set and its complement is closed