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set_theory

# set_theory - NOTES ON SET THEORY The purpose of these notes...

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NOTES ON SET THEORY The purpose of these notes is to cover some set theory terminology not included in Solow’s book. You should read Appendix A.1 in the book before reading these notes. The symbol “:=” means that the thing on the left is being defined as the thing on the right. First, the book defines the notion of the complement, denoted by A c , of a set A in some universal set U . More generally, we can define the complement of a set inside of any other set: Definition 1. Let A and B be sets. The complement of A in B , denoted by B \ A or B - A , is the set of elements of B which are not in A ; in set notation this means B \ A := { x B | x / A } . For example, if Z is the set of integers and 2 Z is the set of even integers (this is a common notation), then Z \ 2 Z is the set of odd integers. We would also like a quick way of saying that two sets have nothing in common. This is given by: Definition 2. We say that two sets A and B are disjoint if they have no elements in common; i.e. if A B = .

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