If you find any mistakes, please make a comment! Thank you.

## Solution to Understanding Analysis Second Edition

### Chapter 1 The Real Numbers

• 1.1 Discussion: The Irrationality of $\sqrt 2$ (no exercises)
• 1.2 Some Preliminaries
• 1.3 The Axiom of Completeness
• 1.4 Consequences of Completeness
• 1.5 Cardinality
• 1.6 Cantor's Theorem
• 1.7 Epilogue (no exercises)

### Chapter 3 Basic Topology of $\mathbf R$

• 3.1 Discussion: The Cantor Set (no exercises)
• 3.2 Open and Closed Sets
• 3.3 Compact Sets
• 3.4 Perfect Sets and Connected Sets
• 3.5 Baire's Theorem
• 3.6 Epilogue (no exercises)

### Chapter 4 Functional Limits and Continuity

#### Linearity

This website is supposed to help you study Linear Algebras. Please only read these solutions after thinking about the problems carefully. Do not just copy these solutions.

### This Post Has 6 Comments

1. Do you have solutions to the second edition?

1. I suspect this is for a different edition than the second, because I looked and the problems don't match in section 1.3

2. Hi, just wondering if you're still updating this website; in particular, by writing up solutions to more problems from "Understanding Analysis". Your work is fantastic and I can't wait to see more coming up in the near future. Thank you so much for your contribution!

1. I will update but not at this moment. I am a little bit busy right now.