Lecture_11_09

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

## This note was uploaded on 02/27/2011 for the course PHILOSOPHY 101 taught by Professor H during the Spring '11 term at Columbia College.

Ask a homework question - tutors are online