🌱 Digital Garden

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