5.7 Outline

A.  Definition
B. Clock arithmetic
      1. addition of a 12-hour clock
      2. elementary operations
          a. subtraction
          b. multiplication
          c. zero multiplication
          d. division
C. Modulo five arithmetic
     1. addition of a 5-hour clock
     2. congruence modulo m
     3. solving modular equations
D. Group properties for a modulo system
     1. testing group properties
     2. testing field properties

5.7 Essential Ideas

Discrete mathematics is that part of mathematics that deals with sets of objects that can be counted or processes that consist of a sequence of individual steps. The set of objects is called finite if the cardinality of the set is a counting number. As an example of a finite algebra, modulo arithmetic is considered.