I apologize for the unclear post earlier. However, that is exactly how the question reads in the book. Let me see if I can clarify.

r+s= {p + q: p inrand q ins}

I need to show that r + s is a real number. I am assuming that I show this by using a Dedekind left set and proving that:

1) r is proper, non-empty subset

2) r is close to the left

3) r has no maximum element

I need to show the same for r x s.

My trouble with this, is that I am inexperienced at writing proofs and often need help with the "acceptable" notion. I am continuing to learn what statements actually prove what I am trying to prove and it is helpful to see another person's thought process. Unfortunately, I go to a university that refuses to teach me "how" to write a proof.

Thanks for the help.