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. 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 … Defining a Set Examples of Set Numerical Sets (Well-Defined) Representation of a Set Famous Sets in Math Finite and infinite Sets Empty Set / Null Set Singleton Set or Unit Set Equal and Equivalent Sets Cardinality of Sets Subsets Power Sets Disjoint Sets Union of Sets Intersection of Sets Complement of a Set. If you wish to opt out, please close your SlideShare account. 2. A set A is said to be subset of another set B if and only if every element of set A is also a part of other set B. Denoted by ‘⊆‘. Subject: Mathematics These notes were prepared using notes from the course taught by Uri Avraham, Assaf Hasson, and of course, Matti Rubin. You can change your ad preferences anytime. De ning a set formally is a pretty delicate matter, for now, we will be happy to consider an intuitive de nition, namely: De nition 24. Eg: (i) The set of all straight line in a given plane. N:= f1;2;:::g, the set of Natural numbers; 3. When we “partition a set,” we break it down into mutually exclusive and exhaustive regions, i.e., regions with no overlap. Edition of August 9, 2017: chapter on proper forcing rewritten. NB (Note Bene) - It is almost never necessary in a mathematical proof to remember that a function is literally a set of ordered pairs. ± The set of positive integers is an infinite set. (iii) The set of real numbers between ‘1’ and ‘2’. 1.The empty set, denoted ?, is the set that has no element. Basic Set Theory The following notations will be followed throughout the book. Any collection of items can form a set. 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. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. We can use these sets understand relationships between groups, and to analyze survey data. •The set of months is a finite set because it has 12 elements. (ii) The set of all natural numbers. We say that a group of sets partitions another set if they are mutually exclusive and exhaustive with respect to that set. Looks like you’ve clipped this slide to already. •a A “a is an element of set A” “a is a member of set A” •a A “a is not an element of set A” • Order of elements is meaningless. “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. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. CONTENTS 5 Preface These notes for a graduate course in set theory are on their way to be- coming a book. 1. Z:= f0;1; 1;2; 2;:::g, the set of Integers; 5. De nition 1.8 (Injection). 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). Ling 409, Partee lecture notes, Lecture 1 September 7, 2005 p. 4 From the definition of identity follows that there exists only one empty set; its identity is fully determined by its absence of members. Set. p. cm. Introduction to Sets It is natural for us to classify items into groups, or sets, and consider how those sets overlap with each other. These lecture notes were prepared with the purpose of helping the students to follow the lectures more easily and e ciently. Note that empty list notation {} is not usually used for the empty set, we have a … An art collector might own a collection of paintings, while a music lover might keep a collection of CDs.


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