Discrete math set theory proofs pdf

For example, the set 2,4,17,23 is the same as the set 17,4,23,2. Definitions and the element method of proof recall that a set is a collection of elements. But even more, set theory is the milieu in which mathematics takes place today. Proof, sets, and logic department of mathematics boise state.

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. 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. Learning how to write mathematical proofs takes time and hard work. A set is an unordered collection of distinct objects. This chapter will be devoted to understanding set theory, relations, functions.

This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. Issues about data structures used to represent sets and the computational cost of set operations. Discrete mathematics, set theory, and logic discrete math, graph theory, combinatorics, recurrence relations difference equations, set theory, gene. Math 522, advanced set theory, at boise state university, on the practical level. An overview of logic, proofs, set theory, and functions. Klostermeyer school of computing university of north florida jacksonville, fl 32224 email. We can list each element or member of a set inside curly brackets like this.

In earlier versions of our logic style manual, we tended to. An important feature of a set is that its elements are \distinct or \uniquely identi able. In fact, this is the only rigorous way to prove that two sets. Set theory basic building block for types of objects in discrete mathematics. The book began as a set of notes for the discrete mathematics course at the. Many different systems of axioms have been proposed. Elements of a set can be just about anything from real physical objects to abstract mathematical objects. The sets shown to exist by this theorem are in a sense discrete they. As with any mathematical proof, the first step is to try to get a handle on how all the pieces move.

Proofs are to mathematics what spelling is to poetry. A set is typically determined by its distinct elements, or members, by. Basic set theory members of the collection comprising the set are also referred to as elements of the set. This alone assures the subject of a place prominent in human culture. Introduction to discrete mathematics stanford ai lab.