Let A be the set of all numbers of the form a+ b[sqt(2)], where a and b are arbitrary rational numbers. Let addition and muliplication be defined on A in the same way they are defined for real numbers. Prove that the set A is a field.
Let A be the set of all numbers of the form a+ b[sqt(2)], where a and b are arbitrary rational numbers. Let addition and muliplication be defined on A in the same way they are defined for real numbers. Prove that the set A is a field.
Well, prove all the field axioms: closure, commutativity, associativity, existence of inverse ,etc....