PPT-Number Theory and Techniques of Proof

Basic definitionsParity An integer n is called even if and only if there exists an integer k such that n 2k An integer n is called odd if and only if it is not even. These three techniques are used to prove statements of the form If then As we know most theorems and propositions have this conditional form or they can be reworded to have this form Thus the three main techniques are quite important But some theo (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. 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. 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. DPLL(T)-Based SMT Solvers. Guy . Katz. , Clark Barrett, . Cesare . Tinelli. , Andrew Reynolds, Liana . Hadarean. Stanford . University. The University. of Iowa. Synopsys. Producing Checkable Artifacts. 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 . (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.. 3.5. Direct Proof and Counterexample. 5. Floor & Ceiling. Floor & Ceiling. Definition. Floor. Given any real number . x. , the floor of . x. , denoted ⎣. x. ⎦, is defined as: . ⎣. x. ⎦ = . 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) Lecture 11. https://abstrusegoose.com/353. Announcements. Lots of folks sounded concerned about English proofs in sections.. THAT’S NORMAL. English proofs aren’t easy the first few times (or the next few times…sometimes not even after a decade…) . 2022. Lecture 11. https://abstrusegoose.com/353. Proof By Cases. Let . . Prime. , . . Odd. . PowerOfTwo. Where . PowerOfTwo. Integer. Prove . We need two different arguments – one for 2 and one for all the other primes…. 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.