apparently an operation on a number with itself.
f: A x B --> C
'groups' without inverse element:
for the set of {0,1} and summation operation it woulde give you
1+1 = 0
for the set of {0,1,2} and summation operation it woulde give you
1+1 = 2
(while here:2+2 = 0)
for groups with inverse element:
for the set of {-1,0,1} and summation operation it woulde give you
1+1=0
-1+(-1)=0
for the set of {-1,-2,0,1,2} and summation operation it woulde give you
1+1=2
-2+(-2) =0
just wanted to state that. restricting the value set can probably result in pretty much everything at 1+1.
https://en.wikipedia.org/wiki/Group_(mathematics) 
