i need to show that when A is a subset of B and B is a subset of R (A B are non empty sets) then: infB<=infA<=supA<=SupB here's what i did: if infA is in A then infA is in B, and by defintion of inf, infB<=infA. if infA isnt in A then for every e>0 we choose, infA+e is in A and so infA is in B, so infA+e>=infB, we can find e'>0 such that infA+e>=infB+e'>infB so we have: infA-infB>=e'-e, let e=e'/2 then we have infA-infB>e'/2>0 so we have infA>infB. (is this method correct?). obviously supA>=infA by defintion. i think that the same goes for supA and supB, with suitable changes.