ABSTRACT
This chapter presents functions and the terms related to them. When drawing diagrams to represent functions, it is not necessary to illustrate every element of the co-domain. Working with functions, images of sets, and inverse images of sets can be a challenge in notation, and that notational struggle often leads to frustrations when trying to figure out how proofs with these objects work. Certain specific functions tend to appear throughout various areas of higher mathematics. Arbitrary functions preserve the union of sets, but they need not preserve the intersection of sets. The term permutation is synonymous with the concept from elementary counting of the same name. In that context, permutations dealt with ordering objects.
