Algebraic Structure
A non-empty set S is called algebraic structure wrt binary operation * if (a*b)∈S ∀a,b∈S
’*’ is a closure operation on S
Examples #
- (N,+): yes
- (N,⋅): yes
- (N,-): no;
- 3-5=-2 ∉N; 3,5∈N
- (N,÷): no
- 3/5∉N; 3,5∈N
- (Z,+,⋅,-): yes
- (R,+,⋅,-,÷): yes
- Q
- (Q,÷):no; 5/0∉Q; 5,0∈Q
- (Q*,÷):yes