Prove that if in an ordered set every non-empty subset, which is bounded from above, has a supremum, then in this set every non-empty subset, which is bounded from below, has an infimum.
I know that any non empty subset which is bounded from above has supremum by definition of upper set and vice versa for lower set but I don't know how to prove the subset of a subset that has supremum, has infimum.
I know that any non empty subset which is bounded from above has supremum by definition of upper set and vice versa for lower set but I don't know how to prove the subset of a subset that has supremum, has infimum.
Last edited: