'Equivalence relation' diaporamas de présentation

Discrete Structures

In The Name of Allah. Discrete Structures. Instructor: Dr. Ali Movaghar. Sharif University of Technology. Fall 1389. Relations : In these slides: Relations and their properties n- ary relations and their applications Representing relations Closures of relations

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Posets, equivalence relations, and functions

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CS201: Data Structures and Discrete Mathematics I

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Number of Faces in Arrangements

Number of Faces in Arrangements. Omar Shibli. Contents. Arrangements of Hyperplanes Arrangements of Other Geometric Objects Number of Vertices of Level at Most k The Zone Theorem The Cutting Lemma Revisited . Arrangements of Hyperplanes. Recall from Section 4.1

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Partial Orderings

Partial Orderings. Based on Slides by Chuck Allison from http://uvsc.freshsources.com/Courses/CS_2300/Slides/slides.html Rosen, Chapter 8.6 Modified by Longin Jan Latecki. Introduction. An equivalence relation is a relation that is reflexive, symmetric, and transitive

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CSE 331 Software Design & Implementation

CSE 331 Software Design & Implementation. Dan Grossman Winter 2014 Identity, equals , and h ashCode (Based on slides by Mike Ernst, David Notkin , Hal Perkins). Object equality. A simple idea?? Two objects are equal if they have the same value

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CS 173: Discrete Mathematical Structures

CS 173: Discrete Mathematical Structures. Cinda Heeren heeren@cs.uiuc.edu Siebel Center, rm 2213 Office Hours: W 12:30-2:30. CS 173 Announcements. Homework #11 available, due 12/04, 8a. Final exam 12/14, 8-11a. Email Cinda with conflicts.

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FORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY

15-453. FORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A. MINIMIZING DFAs. THURSDAY Jan 24. 0. 1. 0. 1. 1. 0. 1. 0. IS THIS MINIMAL?. NO. 0. 1. 1. 0. IS THIS MINIMAL?. THEOREM.

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CSE 331 Software Design & Implementation

CSE 331 Software Design & Implementation. Hal Perkins Autumn 2012 == , equals() , and all that (Slides by David Notkin and Mike Ernst). Programming: object equality. The basic intuition is simple : two objects are equal if they are indistinguishable (have the same value)

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CSCI 115

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Algorithms to Approximately Count and Sample Conforming Colorings of Graphs

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Graphs and Isomorphisms

Graphs and Isomorphisms. Backyards of Old Houses in Antwerp in the Snow Van Gogh. Discrete Structures (CS 173) Madhusudan Parthasarathy, University of Illinois. Administrative. How was the exam? Midterm graded by Friday next week (hopefully)

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Numerical characterizations of covering rough sets based on evidence theory

Numerical characterizations of covering rough sets based on evidence theory. Chen Degang, Zhang Xiao Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206, P. R. China.

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Relations

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Lecture 7

Lecture 7 . Surreal Numbers. The Construction of R from Q . Recall that the set of reals R can be constructed from the set of rationals Q using Cauchy sequences.

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Formal ontology as interlingua: the SUMO and WordNet linking project and global WordNet

Formal ontology as interlingua: the SUMO and WordNet linking project and global WordNet. Adam Pease and Christiane Fellbaum Presenter: ???. Outline. 2.1 WordNet 2.1.1 Types and instances 2.1.2 Formal vs linguistic relations 2.1.3 Lexical vs conceptual ontologies 2.1.4 SUMO

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Equivalence Relations. Partial Ordering Relations

Equivalence Relations. Partial Ordering Relations. Equivalence Relation and Partition. Every equivalence relation on S gives rise to a partition of S by taking the family of subsets in the partition to be the equivalence classes of the equivalence relation.

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CONGRUENCES AND MODULAR ARITHMETIC

CONGRUENCES AND MODULAR ARITHMETIC. Congruence and Modular Arithmetic Definition: a is congruent to b mod n means that n?a -b, (a-b) is divisible by n. Notation: a ? b (mod n) , a, b, n ? I, n ? b Ex . 42 ? 30 (mod 3)

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6. Modular Arithmetic

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Review of Mathematical Notation / Terminology

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