1549901369-Elements_of_Real_Analysis__Denlinger_

Contents xi

9

8.

8.

8.

8.

Series of Products.

Power Series....

Analytic Functions

*Elementary Transcendental Functions (Project).

Sequences and Series of Functions

9.1 Families of Functions and Pointwise Convergence

9.2 Uniform Convergence ................

9.3 Implications of Uniform Convergence in Calculus

9.4 *Two Results of Weierstrass...

9.5 *A Glimpse Beyond the Horizon.

APPENDICES

A Logic and Proofs

A. l The Logic of Propositions........

A.2 The Logic of Predicates and Quantifiers.

A.3 Strategies of Proving Theorems

A.4 Properties of Equality......

B Sets and Functions
B.l Sets and the Algebra of Sets
B.2 Functions ...........
B.3 Algebra of Real-Valued Functions

c Answers & Hints for Selected Exercises

Bibliography

Glossary of Symbols

Index

. 494
. 504
. 519
. 535

541

. 541
. 548
. 557
. 568
. 578

583

583

. 583
. 595
. 606
. 611

613

. 613
. 619
. 625

635

709

719

727