1. Proof by contradiction Po-Shen Loh CMU Putnam Seminar, Fall

Source URL: www.math.cmu.edu

• Functions and mappings
• Calculus
• Mathematical analysis
• Limit of a function
• Continuous function
• Lebesgue integration
• Centroid
• Function
• Metric space
• Non-analytic smooth function

Solutions for Exercises for Propositional Logic 1. Proof by induction. 2. • A tautology: (p ∨ (¬p ∨ (q ∨ (r ∨ s)))) • A contradiction: (p ∧ (¬p ∧ (q ∧ (r ∧ s))))

Source URL: www.mathsummer.philosophie.uni-muenchen.de

An Innocent Investigation D. Joyce, Clark University January 2006 The beginning. Have you ever wondered why every number is either even or odd? I don’t mean to ask if you ever wondered whether every number

Source URL: aleph0.clarku.edu

• Mathematical logic
• Elementary arithmetic
• Mathematical induction
• Singly and doubly even
• Proof by contradiction
• Parity of a permutation
• Handshaking lemma
• Mathematics
• Mathematical proofs
• Parity

CS109A Notes for LectureThe Essence of Proof Mathematical proof is essentially persuasive prose.  Like an essay, it is eective if it convinces the listener.  Also like an essay, we can learn certain rhetorica

Source URL: infolab.stanford.edu

• Propositional calculus
• Rules of inference
• Boolean algebra
• Modus ponens
• Truth table
• Contraposition
• Proof by contradiction
• Vacuous truth
• First-order logic
• Logic
• Mathematics
• Mathematical logic

CS109B Notes for LectureTautologies Logical expressions that evaluate to TRUE for any truth-assignment.  Embody reasoning principles.

Source URL: infolab.stanford.edu

• Mathematical logic
• Logical truth
• Boolean algebra
• Semantics
• Tautology
• Substitution
• Truth table
• Proof by contradiction
• Contradiction
• Logic
• Propositional calculus
• Mathematics

Redirecting Proofs by Contradiction Jasmin Christian Blanchette Technische Universität München, Germany Abstract This paper presents an algorithm that redirects proofs by contradiction. The input is a refutation graph,

Source URL: www21.in.tum.de

• Proof theory
• Automated theorem proving
• Rules of inference
• Mathematical proofs
• Sequent
• Natural deduction
• Proof by contradiction
• Resolution
• First-order logic
• Logic
• Mathematics
• Mathematical logic

Teaching Math More Effectively, Through Calculational Proofs Author(s): David Gries and Fred B. Schneider Source: The American Mathematical Monthly, Vol. 102, No. 8 (Oct., 1995), pp[removed]Published by: Mathematical As

Source URL: www.cs.cornell.edu

• Mathematical proofs
• Model theory
• Logic in computer science
• Proof theory
• Propositional calculus
• Proof by contradiction
• First-order logic
• FO
• Integration by substitution
• Mathematics
• Logic
• Mathematical logic

CHAPTER 3 Proof Techniques 3.1

Source URL: myslu.stlawu.edu

• Mathematical logic
• Rules of inference
• Irrational number
• Proof by contrapositive
• Proof by contradiction
• Contraposition
• Prime number
• Direct proof
• If and only if
• Mathematics
• Mathematical proofs
• Logic

CHAPTER 8 Answers and Hints These pages contain answers to every exercise appearing in the book. Before

Source URL: myslu.stlawu.edu

• Mathematical proofs
• Rules of inference
• Quantification
• Vacuous truth
• Contraposition
• Proof by contrapositive
• Function
• Proof by contradiction
• Universal quantification
• Mathematics
• Logic
• Mathematical logic

PDF Document

Source URL: www.math.wustl.edu

• Proof theory
• Mathematical proofs
• Logical syntax
• Logical truth
• Theorem
• Pythagorean theorem
• Proof by contradiction
• Formal proof
• Mathematical induction
• Mathematics
• Logic
• Mathematical logic