Since is bounded below, is not empty. Every is an upper bound of . So is bounded above which implies that exists in where (e.g. assume has lub property). If then is not an upper bound of . And so . So .
If then . So .
Let be bounded below, and define is a lower bound for . Show that .
This is what I have:
Let . Let be any lower bound for . It follows that . Since for all , is an upper bound for .
Now I need to show that for any other upper bound for , . I think this has to do with showing that any upper bound for B is an element of A, but I can't figure out how to show this.
Thanks for the help,