Let A be a partially ordered set. Suppose A is a subset of B and B is a subset of C. Assuming that all the least upper bounds and greatest lower bounds exist, prove that: glb(B)≤glb(A).
I start you off. If is the greatest lower bound for then for all . But then for all because . This means that where is greatest lower bound for because is a lower bound for and is the greatest lower bound for .
Last edited by ThePerfectHacker; March 31st 2008 at 07:31 PM.