Introduction to Mathematical Proof

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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.

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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