I think is a very dumb question, but i failed to find in the books if this statement is true. One can easily proove that if a ordered set S has the Least Upper Bound Property, then every non empty subset of S, that is bounded from below, has a Greatest Lower Bound in S.
But is equally true, that, if a ordered set M has the Greatest Lower Bound Property, then every non empty subset of M, that is bounded from above, has a Least Upper Bound in M?
Thank's a lot!