Basic Definitions : Group Theory #group theory
Basic Definitions : * Binary Operation * Algebraic Structure * Quasi- Group or Groupoid * Semi Group * Monoid * Group * Abelian Group Binary Operation : Let S be a non-empty set . If f : SxS→R is a mapping , then f is called binary operation or binary composition on S. Thus If a relation in S is such that every pair ( distinct or equal ) of elements of S taken in definite order is associated with a unique element of S then it is called a binary operation in S. Otherwise the relationis not binary operation in S and the relation is simply an operation in S. (a,b) 𝟄 SxS , ∃ a unique element f(a,b) 𝟄 S. We observe that addition, multiplication, subtraction are binary operations in R and division is not a binary operation in R why because division by 0 is not defined...