When we work with a congruence class, we have to keep two key things in mind. First, we have to know what “n” is in the Zn.  This is similar to the base referred to above. When we work with Z3,for example, we are splitting the integers (all of them) into three “classes” by talking about those that are congruent to 0, 1, and 2 (mod 3).  If you remember, the integers that are congruent to 0 are -6, -3, 0, 3, 6, 0…..  What do you notice about those?  Which ones are congruent to 1? What do they have in common?  (And so on.) What you need to notice about these, for now, is that they partition the integers into disjoint subsets.  (Do you see that?)  The other thing you’ll be doing in Section 2.6 is learning to do simple arithmetic with these congruence classes and even solving some simple “equations.” This is a really simple one, but if we take [1] + [2] in our example above does it make sense that we end up with [0]? Can you explain why that happens?

When we work with a congruence class, we have to keep two key things in mind. First, we have to know what “n” is in the Z_n.  This is similar to the base referred to above. When we work with Z₃,for example, we are splitting the integers (all of them) into three “classes” by talking about those that are congruent to 0, 1, and 2 (mod 3).  If you remember, the integers that are congruent to 0 are -6, -3, 0, 3, 6, 0…..  What do you notice about those?  Which ones are congruent to 1? What do they have in common?  (And so on.)

What you need to notice about these, for now, is that they partition the integers into disjoint subsets.  (Do you see that?)  The other thing you’ll be doing in Section 2.6 is learning to do simple arithmetic with these congruence classes and even solving some simple “equations.”

This is a really simple one, but if we take [1] + [2] in our example above does it make sense that we end up with [0]? Can you explain why that happens?