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We have modelled in Chapter Sets, Relations, and Functions functions as special relations, i.e., as sets of tuples. In this chapter, we will elaborate this notion and its properties in more detail and describe some important constructions and applications: we will count set elements and compare the sizes of (also infinite) sets, embed domains into other domains such that the properties of their operations are preserved, model numeric sequences and series, discuss special functions over the reals, and finally compare the asymptotic behavior of functions.