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Part II Sets and Functions

Sets are one of the fundamental structures in mathematics. We present the basic notation and definitions for working with sets, including the important notion of the equality of sets, in Chapter 5.

In Chapter 6 we introduce subsets and explain the construction of sets as Cartesian products of sets.

Functions are another fundamental objects in mathematics. Functions assign each element in one set to an element in another set. Often they are used to change the representation of objects. We investigate properties such as equality and invertibility of functions and combine functions to obtain new functions (Chapter 7).

In Chapter 8 we consider special functions, namely an encoding function that turns characters into numbers, encryption functions and their inverses decryption functions.