proofs progress. These guidelines are introduced as needed and begin in Sec-tion 1.2. This book starts out at a more basic level, dealing with the prin-ciples of “raw logic” before venturing into any specialized field of mathematics. Subsets 11 1.4. PowerSets 14 1.5. There is a short quiz at the end of each chapter. IntroductiontoSets 3 1.2. out the book. P1:OSO/OVY P2:OSO/OVY QC:OSO/OVY T1:OSO A01_CHART6753_04_SE_FM PH03348-Chartrand September22,2017 8:50 CharCount=0 Fourth Edition Mathematical Proofs mathematical logic. mathematical language and symbols before moving onto the serious matter of writing the mathematical proofs. This chart does not include uniqueness proofs and proof by induction, which are explained in §3.3 and §4. [n the belief that beginners should be exposed to the easiest and most natural proofs, I have used free-swinging set-theoretic methods. We provide a handy chart which summarizes the meaning and basic ways to prove any type of statement. Union,Intersection,Difference 17 Guidelines for writing mathematical proofs are incorporated into the book.

Sets 3 1.1. In §2 and §3 we introduce the basic principles for proving statements. 0.4. Appendix A contains a summary of all the guidelines for writing mathematical proofs that are introducedthroughoutthe text. TheCartesianProduct 8 1.3. Advice to the Student Welcome to higher mathematics! You will nd that some proofs are missing the steps and the purple In §1 we introduce the basic vocabulary for mathematical statements. Mathematical proofs are also constructed by combining certain basic proof ... because it is an important subject that is used in the rest of the book (and throughout mathematics), and also because it serves to illustrate many of the points of logic discussed in these chapters. Contents Preface vii Introduction viii I Fundamentals 1. In format, they resemble the questions found in standardized tests. to more advanced classical mathematical structures and arguments as soon as the student has an adequate understanding of the logic under-lying mathematical proofs. This book contains practice quizzes, tests, and exam questions. In addition,ev- Each theorem is followed by the \notes", which are the thoughts on the topic, intended to give a deeper idea of the statement. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical …

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