PPT-Chapter 3 Elementary Number Theory and Methods of Proof

35 Direct Proof and Counterexample 5 Floor amp Ceiling Floor amp Ceiling Definition Floor Given any real number x the floor of x denoted x is defined as x . (aka cs302: Discrete Mathematics II). Spring 2010. University of Virginia. David Evans. Computation is what Computers do, who needs theory?. flickr. : . gastev. [cc]. Charles Babbage’s . Difference Engine. Elementary Number Theory and Methods of Proof. 3.6. Indirect Argument. Reductio. Ad Absurdum. Argument by contradiction. Illustration in proof of innocence . Suppose I did commit the crime. Then at the time of the crime, I would have had to be at the scene of the crime.. This Lecture. Now we have learnt the basics in logic.. We are going to apply the logical rules in proving mathematical theorems.. Direct proof. Contrapositive. Proof by contradiction. Proof by cases. Exploring the Relation between Design & Theory. Kevin . L. . Ladd. 18 May 2010. Conference on Faith and Health. Syddansk. . Universitet. , Odense, . Danmark. 18 May 2010. Mixed Methods, Design, & Theory. Melisha. How He died.. On the night of September 7, 1996, He was shot while in a . bmw. .. He was attending a Mike Tyson Fight. His car was shot at. He was hit In the . thigh,hand,chest,pelvis. (source . (aka cs302: Discrete Mathematics II). Spring 2010. University of Virginia. David Evans. Computation is what Computers do, who needs theory?. flickr. : . gastev. [cc]. Charles Babbage’s . Difference Engine. Eric Ottman. Syracuse University. April 8, 2017. A Tiny Bit of History. In 1874, Georg Cantor published his first article on set theory, including, among other things, his famous “diagonal argument” proving . 1.1 Propositional Logic. 1.2 Propositional Equivalences. 1.3 Predicates and Quantifiers. 1.4 Nested Quantifiers. 1.5 Rules of Inference. 1.6 Introduction to Proofs. 1.7 Proof Methods and Strategy. To prove an argument is valid or the conclusion follows . (aka cs302: Discrete Mathematics II). Spring 2010. University of Virginia. David Evans. Computation is what Computers do, who needs theory?. flickr. : . gastev. [cc]. Charles Babbage’s . Difference Engine. Basic . definitions:Parity. An . integer. n is called . even. . if, and only if. , . there exists . an integer k such that . n = 2*k. .. An integer n is called . odd. if, and only if, . it is not even.. Basic . definitions:Parity. An . integer. n is called . even. . if, and only if. , . there exists . an integer k such that . n = 2*k. .. An integer n is called . odd. if, and only if, . it is not even.. Probabilistic Proof System — An Introduction Deng Yi CCRG@NTU A Basic Question Suppose: You are all-powerful and can do cloud computing (i.e., whenever you are asked a question, you can give the correct answer in one second by just looking at the cloud overhead) Many pieces of software need to maintain sets of items. For example, a database is a large set of pieces of information.. A university maintains a set of all the students enrolled.. An airline maintains a set of all past and future flights. . Now we have learnt the basics in logic.. We are going to apply the logical rules in proving mathematical theorems.. Direct proof. Contrapositive. Proof by contradiction. Proof by cases. Basic Definitions.