Discrete mathematics, set theory, and logic discrete math, graph theory, combinatorics, recurrence relations difference equations, set theory, gene. Proof, sets, and logic department of mathematics boise state. Math 522, advanced set theory, at boise state university, on the practical level. For example, the set 2,4,17,23 is the same as the set 17,4,23,2. The book began as a set of notes for the discrete mathematics course at the. Basic set theory members of the collection comprising the set are also referred to as elements of the set. Issues about data structures used to represent sets and the computational cost of set operations. Klostermeyer school of computing university of north florida jacksonville, fl 32224 email. This chapter will be devoted to understanding set theory, relations, functions. Elements of a set can be just about anything from real physical objects to abstract mathematical objects. The objects in a set are called the elements, or members, of the set. The sets shown to exist by this theorem are in a sense discrete they. A set is typically determined by its distinct elements, or members, by.
Learning how to write mathematical proofs takes time and hard work. Continued since each set is a subset of the other, we have established the equality of the two sets so a b c a b \a c. A set is an unordered collection of distinct objects. This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. An overview of logic, proofs, set theory, and functions. Mat231 transition to higher math proofs involving sets fall 2014 8 11. Definitions and the element method of proof recall that a set is a collection of elements. Proofs are to mathematics what spelling is to poetry. Introduction to discrete mathematics stanford ai lab. Sets we discussed in class how to formally show that one set is a subset of another and how to show two sets are equal. 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. An important feature of a set is that its elements are \distinct or \uniquely identi able. Discrete mathematics amit chakrabarti proofs by contradiction and by mathematical induction direct proofs at this point, we have seen a few examples of mathematical proofs.
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