6 generality for functions defined on arbitrary subsets of R, the main results are stated and proved for functions defined on intervals. We leave the notions of open sets, closed sets and compact sets to Chapter 5. We also moved to this chapter various results about continuous functions defined on compact sets. A second important feature of this edition is the addition of more detailed explanations on various techniques for proving limits (of sequences and of functions) directly from the definition. These explanations are intended to make the text more welcoming for students who are tackling various proofs in analysis for the first time. Finally, we corrected a number of typos that have stubbornly persisted in the second edition. We have used these notes multiple times to teach the one-quarter course Introduction to Mathematical Analysis I at Portland State University. We are currently completing the second volume that will include Riemann integration and series as well as additional special topics for exploration. Acknowledgements We would like to thank our colleagues in the Fariborz Maseeh Department of Mathematics and Statistics for their constructive feedback and thoughtful insights. We also want to acknowledge the many students in our courses who offered suggestions. Finally, we give special thanks to Karen Bjork, Head of Digital Initiatives, Cataloging, & eAccess at the Portland State University Library, for her continuing support for this project. The creation and update of this textbook were supported in part by a PSU faculty enhancement grant and by an OER grant.
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