set theory lecture notes ppt

Edition of November 14, 2016: chapter on proper forcing changed; the proof of The-orem 28.5 was in error, and a new proof using a game is given (Theorem 28.33). You can change your ad preferences anytime. Basic Set Theory The following notations will be followed throughout the book. These lecture notes were prepared with the purpose of helping the students to follow the lectures more easily and e ciently. Looks like you’ve clipped this slide to already. Example ± For S= {1,2,3} CONTENTS 5 Preface These notes for a graduate course in set theory are on their way to be- coming a book. BASIC CONCEPTS OF SETS Content Define a set Represent a set Define the number of elements of a set Practice Problems 1 Compare sets Recognize different types of set Practice Problems 2 Define the subsets of a set Review Exercises 1 OPERATIONS ON SETS Determine the union of two or more sets Practice Problems 3 Determine the intersection of two or more sets Practice Problems 4 Determine the complement of a set Determine the difference of two sets Practice Problems … Cynthia Church pro- duced the first electronic copy in December 2002. Z:= f0;1; 1;2; 2;:::g, the set of Integers; 5. LECTURES ON SET THEORY J. Donald Monk March 11, 2019 i. “A revised and corrected republication of Set Theory, originally published in 1971 by Addison-Wesley Publishing Company, Reading, Massachusetts.” Summary: “This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. De nition 1.8 (Injection). We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. See our Privacy Policy and User Agreement for details. See our User Agreement and Privacy Policy. ± The set of prime numbers is an infinite set. Q:= fp q: p;q2Z;q6= 0 … (iii) The set of real numbers between ‘1’ and ‘2’. Clipping is a handy way to collect important slides you want to go back to later. As of this date, Scribd will manage your SlideShare account and any content you may have on SlideShare, and Scribd's General Terms of Use and Privacy Policy will apply. Each An art collector might own a collection of paintings, while a music lover might keep a collection of CDs. When we “partition a set,” we break it down into mutually exclusive and exhaustive regions, i.e., regions with no overlap. Preface Edition of March 11, 2019: chapter on p = t rewritten. They are not guaran-teed to be comprehensive of the material covered in the course. Example: {x x is a natural number and x < 8} Reading: “the set of all x such that x is a natural number and is less than 8” So the second part of this notation is a prope rty the members of the set share (a condition Defining a Set • The symbol ‘∈’ is used to denote belongs to or is an element of or is a member of set. We say that a group of sets partitions another set if they are mutually exclusive and exhaustive with respect to that set. Set Theory \A set is a Many that allows itself to be thought of as a One." Introduction to Sets Infinite set: A set which is not a finite set, i.e., a set consisting of infinite number of elements is called an infinite set. ‘A ⊆ B ‘ denotes A is a subset of B. Set Partition Definition. James Talmage Adams produced the copy here in February 2005. NB (Note Bene) - It is almost never necessary in a mathematical proof to remember that a function is literally a set of ordered pairs. 1.The empty set, denoted ?, is the set that has no element. We can use these sets understand relationships between groups, and to analyze survey data. Subset. The Note: | | = 0 Power Set power set P(S) of a given set S is the set of all subsets of S: P(S) = { A | A S}. It is natural for us to classify items into groups, or sets, and consider how those sets overlap with each other. ± The set of positive integers is an infinite set. They originated as handwritten notes in a course at the University of Toronto given by Prof. William Weiss. Scribd will begin operating the SlideShare business on December 1, 2020 Note that empty list notation {} is not usually used for the empty set, we have a … If you continue browsing the site, you agree to the use of cookies on this website. Set. Lecture Slides By Adil Aslam. To prove A is the subset of B, we need to simply show that if x belongs to A then x also belongs to B.

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