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Posted 31 January 2008

SETS

This is the head of the chapter on sets.

The concept of set was introduced in the late nineteenth century by Georg Cantor.   It was initially fiercely resisted, but has had such clarifying power that it is now used everywhere in mathematics.  

Informally, a set is a collection of items.  The items which constitute a particular set are called the elements or members of the set. 

¨  Any type of data determines a set  the set of all data of that type. Thus there is a set of integers, a set of numbers, a set of letters of the English alphabet, and so on. 

¨  A set can be any arbitrary collection of math objects.  For example, there is the set containing just the numbers 1,3 and  and nothing else.  

Contents

Sets: Notation

    Russell’s paradox

Some specific sets

Sets: Specification

Sets: Rules of Inference

Sets: Metaphors and images

Operations on sets (incomplete)