On sets and abstract algebra


Abstract algebra has some interesting properties - the theory assumes that in every set we can define 
 a function with two arguments and one result, all three belonging to a same set:

F(a,b) = c

Real world example could be the set of integers and function called a plus
   PLUS(a,b) = a + b

 Arguments and result all belong to the same set. 
 In this theory the set and function with it is called algebraic structure or just algebra.

   Function belonging to the structure is defined as operation.
     For example: 
      A set of elements  {0,1,2}
       A function f(a,b) = a mod b
        Combining those two we have < {0,1,2} , f >