Sets, Relations and Functions
This chapter provides an introduction to fundamental building blocks in mathematics such as sets, relations and functions. Sets are collections of well-defined objects; relations indicate relationships between members of two sets A and B; and functions are a special type of relation where there is exactly (or at most) one relationship for each element a ϵ A with an element in B. A set is a collection of well-defined objects that contains no duplicates. A binary relation R (A, B) where A and B are sets is a subset of the Cartesian product (A × B) of A and B. A total function f: A → B is a special relation such that for each element a ϵ A there is exactly one element b ϵ B. This is written as f(a) = b. A partial function differs from a total function in that the function may be undefined for one or more values of A.
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