That depends on your set, in some cases you get 4 or 0 or prety much anything you want.
for example:
Lets say tha Z. ={0,1} is the set of all the remainings of the division with 2
we got 0=0, 1=1 , 2=0 because if we divide it with 2 we got a remaining of 0
so 3=1,4=0,5=1 and so on
That means tha 2+2=4=0 in Z. , well if we solve the same problem in R we get of course 2+2=4
you can do the ''same'' thing with many options to get any result you want
Lets say Z..={0,1,2,3,4} is the set of all the remainings of the division with 5
then 2+2=4=4 but 2+2+2=6=1
these are just some simple examples, things can get more complicated if you want :p
