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Lecture Notes for MATH 3034 - Introduction to Proofs with Arnold at Virginia Tech (VT)

Notes Information

Material Type:Class Note
Professor:Arnold
Class:MATH 3034 - Introduction to Proofs
Subject:Mathematics
University:Virginia Polytechnic Institute And State University
Term:--
Keywords:
  • Either...or
  • Provided That
  • Contrapositive
  • Particularly
  • Definitions
  • Conjunction
  • Exclusive Or
  • Real Number
  • Contradiction
  • Implications
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Sample Document Text

?? ????????????????????????????? AN INTRODUCTION TO MATHEMATICAL PROOFS NOTES FOR MATH 3034 Jimmy T. Arnold ????????????????????????????? i TABLE OF CONTENTS CHAPTER 1: The Structure of Mathematical Statements .............................1 1.1. Statements .................................................................. 1 1.2. Statement Forms, Logical Equivalence, and Negations ........................ 8 1.3. Quantifiers ................................................................. 15 1.4: Definitions ..................................................................21 CHAPTER 2: Methods of Proof .....................................................26 2.1. Basic Proofs with Quantifiers ...............................................26 2.2. Basic Proofs with Mixed Quantifiers ........................................31 2.3. Implications ................................................................35 2.4. Proofs by Contradiction and Equivalent Statements .........................41 2.5...

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