Equivalence Relations and Zn
Jonathan K. Hodge · 2013
Preview Activity 5.1. When working with large sets of objects, it is often useful to group these objects according to some common attribute or property. For instance, in a cooler containing 100 cans of soft drinks, there may be 30 cans of Coke, 30 cans of Pepsi, and 40 cans of 7 Up. If someone wanted to drink a can of Coke, they probably would not care exactly which can of Coke they pulled out of the cooler. In other words, they would probably consider all of the different cans of Coke to be indistinguishable, or equivalent. This same kind of grouping can be applied to a set of mathematical objects by defining an equivalence relation. In this preview activity, we will investigate how congruence can be used to define such a relation on the integers.