p. cm. Usually we denote sets with upper-case letters, elements with lower-case letters. The elements of a set are the objects in a set. Introduction to Set Theory James H. Steiger. Course Notes Page 1. ± Note: z { } A=B x(x A l x B) ± Two sets A, B are equal iff they have the same elements. The set of even integers can be written: {2n : n is an integer} The opening and closing curly braces denote a set, 2n Primitive Concepts. A Set is any well defined collection of “objects.” Definition. This chapter will be devoted to understanding set theory, relations, functions. Sets are often speciﬁed with curly brace notation. Usually we denote sets with upper-case letters, elements with lower-case letters. We start with the basic set theory. 1.1 Sets Mathematicians over the last two centuries have been used to the idea of considering a collection of objects/numbers as a single entity. PDF. A book of set theory / Charles C Pinter. 110 CHAPTER 4. An Introduction to Elementary Set Theory Guram Bezhanishvili and Eachan Landreth 1 Introduction In this project we will learn elementary set theory from the original historical sources by two key gures in the development of set theory, Georg Cantor (1845{1918) and Richard Dedekind (1831{1916). Sets Definition. The second collection is called a multiset. Set Theory and Logic: Fundamental Concepts (Notes by Dr. J. Santos) A.1. Because music employs a set of pitches (ranging from low to high), the staff acts like a map for the notes--allowing us to hear, read or write them as: Lower Itis perhaps best to say that an extensional deﬁnition of a set is one that is givenbyanenumera-tion (listing) of all its elements. Set Theory and Logic: Fundamental Concepts (Notes by Dr. J. Santos) A.1. They are not guaran-teed to be comprehensive of the material covered in the course. Theorem 1.4. This means that {1,2,3} is a set but {1,1,3} is not because 1 appears twice in the second collection. 2.1 Set Theory A set is a collection of distinct objects. That is, we admit, as a starting point, the existence of certain objects (which we call sets), which we won’t deﬁne, but which we assume satisfy some basic properties, which we express as axioms. They originated as handwritten notes in a course at the University of Toronto given by Prof. William Weiss. The theory of sets is a vibrant, exciting math­ ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. The set theoretic di erence AnBis de ned by x2AnBi x2Aand x62B. Introduction to Logic and Set Theory-2013-2014 General Course Notes December 2, 2013 These notes were prepared as an aid to the student. These notes for a graduate course in set theory are on their way to be-coming a book. Although this is not sufﬁciently well appreciated, it is difﬁcult to give a general characterization of extensional deﬁnitions. Notes represent sounds called pitches. A Set is any well defined collection of “objects.” Definition. Subsets A set A is a subset of a set B iff every element of A is also an element of B.Such a relation between sets is denoted by A ⊆ B.If A ⊆ B and A ≠ B we call A a proper subset of B and write A ⊂ B. The elements of a set are the objects in a set. The technique of using the concept of a set to answer questions is hardly new. Introduction. “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. 1. AzB x(x A l x B) { x [(x A x B) (x B x A)] James Talmage Adams In mathematics, the notion of a set is a primitive notion. The notion of set is taken as “undefined”, “primitive”, or “basic”, so we don’t try to define what a set is, but we can give an informal description, describe Basic Concepts of Set Theory. ± The empty set is denoted by or by { }. Sets and elements Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. Notation. 1.1. Elements of Set Theory eleven; all oxygen molecules in the atmosphere; etc. a staff with no notes on it Each line or space on the staff is for its own note. Let xbe arbitrary. SET THEORY Empty Set The set that contains no element is called the empty set or null set . What this book is about. These entities are what are typically called sets. These notes were prepared using notes from the course taught by Uri Avraham, Assaf Hasson, and of course, Matti Rubin. The five horizontal lines on which the notes sit are called a staff. Cynthia Church pro-duced the ﬁrst electronic copy in December 2002. Notation. Primitive Concepts. Ling 310, adapted from UMass Ling 409, Partee lecture notes March 1, 2006 p. 4 Set Theory Basics.doc 1.4. (Caution: sometimes ⊂ is used the way we are using ⊆.) Free PDF download of Class 11 Maths revision notes & short key-notes for Sets of Chapter 1 to score high marks in exams, prepared by expert mathematics teachers from latest edition of CBSE books.