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Chapter 13 Binary Operations

Binary operations generalize the concept of operations that you have encountered already, such as addition, subtraction, multiplication, and addition.  More precisely formulated a binary operation is a function on a set that combines two elements of the set to form a third element of the set.
In this chapter, after formally defining binary operations, we consider four properties  of the binary operations,  that we have already encountered in special cases. These properties are:
  1. Existence of an identity element,
  2. Existence of inverses,
  3. Associativity, and
  4. Commutativity
Exactly theses properties are also the subjects of the sections in the chapter: