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7 More on Relations

In Chapter Sets, Relations, and Functions, we have introduced relations as subsets of Cartesian products. In this chapter, we focus on binary relations and demonstrate some important applications of this notion. First, we introduce equivalence relations as a tool to partition sets into classes and show how in this way modular arithmetic and various number domains can be defined. Then we deal with relations that help us to impose order structures on sets; finally we show how graphs can be formalized as binary relations.