1. The problem statement, all variables and given/known data I was asked to prove the axioms of a field. so, if we look at the first one: commutativity: a+b=b+a and a*b=b*a where a and b belong in the set of the field 2. Relevant equations 3. The attempt at a solution it's tempting to just substitute values but i know this is the wrong approach since this wouldnt prove the axiom for all values in the set. so im stuck.