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## Homework Statement

Let A, B,be two non empty sets of real numbers with supremums 'alpha' and 'beta' respectively, and let the sets A+B and AB be defined by: A+B={a+b / a belongs to A, b belongs to B}, AB= {ab / a belongs to A, b belongs to B}.

Show that alpha+beta is a supremum of A+B.

## Homework Equations

## The Attempt at a Solution

Im not really sure how to go about this question. Maybe use the completness axion, all real numbers satisfy it, which means that A+B must have a supremem...