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Basic Set Theory - Department of Mathematics

Chapter 2 Basic Set TheoryA set is a Many that allows itself tobe thought of as a Georg CantorThis chapter introduces set Theory , mathematical in-duction, and formalizes the notion of mathematicalfunctions. The material is mostly elementary. Forthose of you new to abstract Mathematics elementarydoes not meansimple(though much of the materialis fairly simple). Rather, elementary means that thematerial requires very little previous education to un-derstand it. Elementary material can be quite chal-lenging and some of the material in this chapter, ifnot exactly rocket science, may require that you ad-just you point of view to understand it. The singlemost powerful technique in Mathematics is to adjustyour point of view until the problem you are tryingto solve becomes point at which this material may divergefrom your previous experience is that it will requireproof.

ever, the central tool of mathematics. This text is for a course that is a students formal introduction to tools and methods of proof. 2.1 Set Theory A set is a collection of distinct objects. This means that {1,2,3} is a set but {1,1,3} is not because 1 appears twice in the second collection. The second collection is called a multiset.

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