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Introduction to Mathematical Proof

Introduction to Mathematical ProofMath 299 Lecture NotesKen Monks - Spring 2021c 2021 - Ken MonksIntroduction toMathematicalProofDr. Monks- University ofScrantonContents0 Introduction31 What is a Proof ? Formal Proof Systems.. Environments and Statements..62 The Language of Identifiers, Variables, and Constants.. Expressions and Statements.. Substitution and Lambda Expressions..103 Rules of Inference in Template Notation for Rules of Inference..114 Propositional The Statements of Propositional Logic.. The Rules of Propositional Logic.. Formal Proof Style..165 Predicate Quantifiers.. Statements.. Declarations.. Rules of Inference.. Equality..216 Proof Shortcuts and Semiformal Use Theorems as Rules of Inference.. Substitute Logically Equivalent Expressions.. Use Famous Logic Theorems Freely.. Identify Certain Statements.. Skip Some Logical Rules of Inference.. Omit Most Premise Citations, Line Labels, and End-of-Subproof Symbols.

Introduction to Mathematical Proof Lecture Notes 1 What is a proof? Simply stated A proof is an explanation of why a statement is objectively correct. Thus, we have two goals for our proofs. •Veracity - we want to verify that a statement is objectively correct. •Exposition - we want to be able to effectively and elegantly explain why it is correct. However, these two goals are …

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