Thread: Proving 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.

Originally Posted by summerset353

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....

Tonio

how would I do that? That is what I am confused about doing.

For example, if you want to show the set is closed under addition, just take two arbitrary elements of the set and add them. What do you get?

Did you even try anything?