Basic set theory a set is a many that allows itself to be thought of as a one. Georg cantor this chapter introduces set theory, mathematical induction, and formalizes the notion of mathematical functions. This series of lessons cover the essential concepts of math set theory the basic ways of describing sets, use of set notation, finite sets, infinite sets, empty sets, subsets, universal sets, complement of a set, basic set operations including intersection and union of sets, using venn diagrams and simple applications of sets. Basic concepts of set theory, functions and relations. Describe the following sets in both formal and informal ways.
The axioms of set theory, ordinal and cardinal arithmetic, the axiom of foundation, relativisation, absoluteness, and reflection, ordinal definable sets and inner models of set theory, the constructible universe l cohens method of forcing, independence. Then by the axiom schema of comprehension, there is a set bdf x2vw g. These notes were prepared using notes from the course taught by uri avraham, assaf hasson, and of course, matti rubin. The purpose of this module is to introduce language for talking about sets, and some. This note is an introduction to the zermelofraenkel set theory with choice zfc.
Free set theory books download ebooks online textbooks. The relationship between set inclusion and the above set operations follows. Here we are going to see some practice questions on set theory. They are not guaranteed to be comprehensive of the material covered in the course. Set theory \a set is a many that allows itself to be thought of as a one. Formal set notation description informal english description 2, 4, 6, 8, 10, the set of all positive even integers, 3, 1, 1, 3, the set of all odd integers n. But even more, set theory is the milieu in which mathematics takes place today. This alone assures the subject of a place prominent in human culture. In mathematics, the notion of a set is a primitive notion.
Introduction to logic and set theory 202014 general course notes december 2, 20 these notes were prepared as an aid to the student. Each of the above laws follows from an analogous logical law. For those of you new to abstract mathematics elementary does not mean simple though much of the material. Schaums outline set theory pdf free download download. An introduction to set theory university of toronto. There are two methods of representing a set i roaster or tabular form ii set builder form 1.
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