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Solutions Manual for Analysis with an Introduction to Proof, 5th Edition
Author: Steven R. Lay (2012)
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ISBN: 9780137546138
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Chapter 1. Logic and Proof
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Chapter 2. Sets and Functions
Chapter 3. The Real Numbers
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Chapter 4. Sequences
Chapter 5. Limits and Continuity
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Chapter 6. Differentiation
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Chapter 7. Integration
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Chapter 8. Infinite Series
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, Instructor’s Solutions Manual
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ANALYSIS
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5th Edition
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Steven R. Lay
Lee University
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Upper Saddle River, New Jersey 07458
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Copyright © 2014 Pearson Education, Inc.
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This manual is intended to accompany the 5th edition of Analysis with an Introduction to Proof
by Steven R. Lay (Pearson, 2013). It contains solutions to nearly every exercise in the text. Those
exercises that have hints (or answers) in the back of the book are numbered in bold print, and the hints
are included here for reference. While many of the proofs have been given in full detail, some of the
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more routine proofs are only outlines. For some of the problems, other approaches may be equally
acceptable. This is particularly true for those problems requesting a counterexample. I have not tried
to be exhaustive in discussing each exercise, but rather to be suggestive.
Let me remind you that the starred exercises are not necessarily the more difficult ones. They
are the exercises that are used in some way in subsequent sections. There is a table on page 3 that
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indicates where starred exercises are used later. The following notations are used throughout this
manual:
= the set of natural numbers {1, 2, 3, 4, …}
= the set of rational numbers
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= the set of real numbers
= “for every”
= “there exists”
= “such that”
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I have tried to be accurate in the preparation of this manual. Undoubtedly, however, some
mistakes will inadvertently slip by. I would appreciate having any errors in this manual or the text
brought to my attention.
Steven R. Lay
PR
OV
ED
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Copyright © 2014 Pearson Education, Inc.
ED
OV
PR
AP
?_
IA
UV
ST
, TABLE OF CONTENTS
Solutions Manual for Analysis with an Introduction to Proof, 5th Edition
Author: Steven R. Lay (2012)
ST
ISBN: 9780137546138
L
Chapter 1. Logic and Proof
A
UV
Chapter 2. Sets and Functions
Chapter 3. The Real Numbers
U
Chapter 4. Sequences
Chapter 5. Limits and Continuity
N
Chapter 6. Differentiation
IA
Chapter 7. Integration
A
Chapter 8. Infinite Series
M
?_
S
AP
N
IO
PR
T
U
OV
L
SO
ED
??
, Instructor’s Solutions Manual
to accompany
ST
UV
ANALYSIS
with an Introduction
to Proof
IA
5th Edition
?_
AP
Steven R. Lay
Lee University
PR
OV
&RS\ULJKW3HDUVRQ(GXFDWLRQ,QF
ED
Upper Saddle River, New Jersey 07458
??
Copyright © 2014 Pearson Education, Inc.
, 2
ST
This manual is intended to accompany the 5th edition of Analysis with an Introduction to Proof
by Steven R. Lay (Pearson, 2013). It contains solutions to nearly every exercise in the text. Those
exercises that have hints (or answers) in the back of the book are numbered in bold print, and the hints
are included here for reference. While many of the proofs have been given in full detail, some of the
UV
more routine proofs are only outlines. For some of the problems, other approaches may be equally
acceptable. This is particularly true for those problems requesting a counterexample. I have not tried
to be exhaustive in discussing each exercise, but rather to be suggestive.
Let me remind you that the starred exercises are not necessarily the more difficult ones. They
are the exercises that are used in some way in subsequent sections. There is a table on page 3 that
IA
indicates where starred exercises are used later. The following notations are used throughout this
manual:
= the set of natural numbers {1, 2, 3, 4, …}
= the set of rational numbers
?_
= the set of real numbers
= “for every”
= “there exists”
= “such that”
AP
I have tried to be accurate in the preparation of this manual. Undoubtedly, however, some
mistakes will inadvertently slip by. I would appreciate having any errors in this manual or the text
brought to my attention.
Steven R. Lay
PR
OV
ED
??
Copyright © 2014 Pearson Education, Inc.
