Lecture_11_09 - Lectures 11 Lectures 11 Basic Concepts 1...

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Unformatted text preview: Lectures 11 Lectures 11 Basic Concepts 1 Basic Concepts 1 A set is any collection of objects, considered as a single abstract object. (p. 154) Membership Extensionality Ways of denoting sets 1. 2. listing defining condition Basic Concepts 2 Basic Concepts 2 Subsets Intersections Unions Relative complement Basic Concepts 3 Basic Concepts 3 Cartesian products Relations Functions 1. 2. “one to one” “onto” Equinumerous sets Inductively defined sets Inductively defined sets Top down Bottom up Examples: natural numbers, language of PL. Define the following using zero and the successor function: {(x,y) : x < y} {(x,y,z) : x,y,z, ∈ N and x+y = z} Proof by induction Proof by induction Statement of the principle Why it works Examples Exam 1 Exam 1 Score 85­100 70­84 55­69 40­54 40 < Number 35 26 12 7 4 Grade A range B range C range D range F ...
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