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
Analysis WebNotes by John Lindsay Orr.
Comments to the author: jorr@math.unl.edu
All contents copyright (C) 1996 John L. Orr University of Nebraska--Lincoln All rights reserved
Last modified: June 16, 1996