Transcription of Sets and Functions - University of California, Davis
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Sets and Functions - University of California, Davis
Chapter 1. Sets and Functions We understand a set to be any collection M of certain distinct objects of our thought or intuition (called the elements of M ) into a whole. (Georg Cantor, 1895). In mathematics you don't understand things. You just get used to them. (Attributed to John von Neumann). In this chapter, we define sets, Functions , and relations and discuss some of their general properties. This material can be referred back to as needed in the subsequent chapters. Sets A set is a collection of objects, called the elements or members of the set. The objects could be anything (planets, squirrels, characters in Shakespeare's plays, or other sets) but for us they will be mathematical objects such as numbers, or sets of numbers.
The de nitions of union and intersection extend to larger collections of sets in a natural way. De nition 1.5. Let Cbe a collection of sets. Then the union of Cis [C= fx: x2Xfor some X2Cg; and the intersection of Cis \ C= fx: x2Xfor every X2Cg: If C= fA;Bg, then this de nition reduces to our previous one for A[Band A\B.
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