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Chapter 13 Binary Operations
Objectives
Show that there is an identity with respect to a binary operation.
Show that an element has an inverse with respect to a binary operation.
Recognize whether a binary operation is associative.
Show that a binary operation is commutative.
Binary operations extend operations you have already seen, such as addition, subtraction, multiplication, and addition. More exactly, a binary operation is a function on a set. It combines two elements of the set to form a third element of the set.
This chapter gives a formal definition of binary operations. It then studies four properties that we have already seen in special cases:
Existence of an identity element,
These same properties are also the topics of the sections in this chapter:
