Verify Prealgebra Axioms

  • Specify the set S and operation * : S x S -> S.
  • Check closure by verifying the result stays in S for representative inputs.
  • Test associativity with a symbolic check or explicit counterexample search.
  • If claiming a monoid, identify the candidate identity element and verify both sides.
  • Record which axioms hold and name the strongest structure justified by them.