Unformatted text preview: a i in turn and deciding whether or not to include it in X . This gives us n independent choices between two possibilities: in X or out. The number of different subsets we can form is therefore 2 n . An alternative way of explaining this is to assign a or 1 to all the elements a i . Each subset corresponds to a unique binary number with n digits. There are 2 n such posibilities. Another proof will be given in the reasoning course next term, using the socalled ‘induction principle’. ± 2.2.5 Introducing Products The last set construct we consider is the product of two (or arbitrary n ) sets. This constructor forms an essential part of the deFnition of relation discussed in the next section. If we want to describe the relationship ‘John loves Mary’, then we require a way of talking about John and Mary at the 11...
View
Full Document
 Spring '09
 Koskesh
 Math, Empty set

Click to edit the document details