# Least upper bound problem

## Homework Statement

Find subsets E$$\subset$$S1$$\subset$$S2$$\subset$$S3$$\subset$$Q such that E has a least upper bound in S1, but does not have any least upper bound in S2, yet does have a least upper bound in S3.

## The Attempt at a Solution

I got totally stuck with it. If a$$\in$$S1 is the least upper bound of E, does that mean a is also in S2 and hence a least upper bound of E in S2?
On the other hand, if E has a least upper bound b in Q, is b unique? So in any subset S of Q, just check if b is in S to see if E has a least upper bound in S?
Thanks a lot

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Dick
O I got it now....So S2=union(S1,{x$$\in$$Q|x^2>2, 0<=x<=2}) would work. And S3=union(S2,{1.1})