Let A,B be subsets of an ordered field F

Let A+B denote the set {(x+y)|x is in A, y is in B)}

Let q=sup A, p=sup B

Show that supA+B = q+p

If this were a test question (which it isn't!), and I turned the following in, what grade do you think would I receive and why?.

Here is what I need to show:

- this says that (q+p) is an upper bound

- this says that nothing less than (q+p) is an upper bound

Here is the proof:

( by definition )

( by definition )

(so (i) is true)

(By definition)

(By definition)

( note: t1 < p t2<q )

So (ii) is true

Therefore sup A+B = q+p

Thanks :-)

I am trying to go thru a book on my own before school starts, but I am always worried because there is no answer key.