'Induction principle' presentation slideshows

Proof by Induction

Proof by Induction. Agenda. Mathematical Induction Proofs Well Ordering Principle Simple Induction Strong Induction (Second Principle of Induction). Mathematical Induction. Suppose we have a sequence of propositions which we would like to prove:

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Syntax With Binders

Syntax With Binders. COS 441 Princeton University Fall 2004. Quick Review About Binding. Difference between bound and free variables ? x . ( x + y ) ? -equivalence ?x. x = ? ?y. y Capture avoiding substitution (( ? x.(x + y)) x) ! (( ? z. (z + y)) x) ! ? z. (x + y).

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Order in the Integers

Order in the Integers. Characterization of the Ring of Integers. Let Z be the set of integers and +, ? be the binary operations of integer addition and multiplication. (Z,+,?) is a commutative ring with unity What other properties of (Z,+,?) distinguish it from other rings?.

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Induction proofs

Induction proofs. To prove that some proposition P ( n ) is true for all n ? n 0 by induction on n ? n 0. 1. Basis : Check that P ( n 0 ) is true. 2. Inductive step . Assume that P ( n ) is true for n = k , where k is some integer, k ? n 0

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Types and Programming Languages

Types and Programming Languages. Lecture 3. Simon Gay Department of Computing Science University of Glasgow. 2006/07. Avoiding run-time errors. We will say that e ? Expr is valid if whenever it reduces to a stuck expression s , s is a value.

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Mathematical Induction.

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Coinduction in a language and verifier

Coinduction in a language and verifier. K. Rustan M. Leino Research in Software Engineering ( RiSE ) Microsoft Research, Redmond. IFIP WG 2.3 meeting Seattle, WA, USA 16 July 2012. Question. How to add coinductive features , like coinductive datatypes c orecursive functions

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Induction and Recursion.

Induction and Recursion. Recursive definition. Explicit definition. Factorial. Geometric progression. Power of relation on a set. The recursive definition of a function makes reference to earlier versions of itself. The main connection between recursion and induction is that

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Recursion and Induction

Recursion and Induction. Define sets by induction zero ? N n ? N ? succ( n ) ? N Define functions on sets by recursion ? n ? N : plus(zero, n ) = n ? m, n ? N : plus(succ( m ), n ) = succ(plus( m , n ))

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Recursion and Induction

Recursion and Induction. Define sets by induction zero ? N n ? N ? succ( n ) ? N Define functions on sets by recursion ? n ? N : plus(zero, n ) = n ? m, n ? N : plus(succ( m ), n ) = succ(plus( m , n ))

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Power System Analysis/ Power System 1 EEE 4113/ EEE 3131

Power System Analysis/ Power System 1 EEE 4113/ EEE 3131. Protective Relay Lecture taken By Kazi Md. Shahiduzzaman Lecturer, EEE, NUB. Outline of this chapter. To Define the protective relay The working principle of protective relay The fundamental requirements of protective relay

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