MATH 415: Introduction to Real Analysis

Fall 2003 Humboldt State University Prof. Freedman

Errata/Suggestions for S. R. Lay’s Analysis with an Introduction to Proof, 3^rd edition

Many thanks to Ms. Jennifer Burman for most of these corrections/suggestions! These are just for the chapters covered in Math 415.

There are also corrections/errata for the rest of the book. See me if you would like a copy of those as well.

p. 112 Answer to Practice Problem 12.4: Replace “Any real number…” with “Any positive real number…”.

p. 124 Last line: Replace “Exercise 5.16(d)” with “Exercise 5.18(d)”.

p. 126 The sixth line from the bottom should again be “Exercise 5.18(d)”

p. 126 Sixth line from the bottom is also missing a period.

p. 126 Theorem 14.7: For clarity, replace “any finite subfamily…” with “every finite subfamily…”

p. 159: Line 8 from the bottom: Replace with .

p. 167: Line 6 of proof of Theorem 19.14: Replace “” with “”.

p. 181 Definition 21.1: Replace “” with “”.

p. 192 Line 4 of proof of Theorem 22.10: The statement “for some ” should be replaced with

“for some between and ”, since we don’t know that . This inequality could also be assumed to hold,

without loss of generality, but this should be stated explicitly.

p. 196 Sixth line of Example 23.4: Replace “” with “”.

p. 278 Proof of Theorem 33.8: In the first line, replace “Theorem 19.10(a)” with “19.11(a)”.

p. 281 Proof of Theorem 33.16: In formula on line 12 from the bottom of the page, replace “” with “”.

In fact, this part of the proof can be replaced with the following simpler argument: Since , and ,

we know that , and so by limit laws, .

p. 284 Exercise 33.14: Replace “Theorem 19.10” with “Theorem 19.11”.

p. 288 Sixth line from the top: In the expression, replace “” with “”.