Let $\mathbb{Q}$ denotes the set of rational numbers. Find sets $E \subset S_1 \subset S_2 \subset S_3 \subset \mathbb{Q}$ such that $E$ has a least upper bound in $S_1$, but does not have a least upper bound in $S_2$, yet does have a least upper bound in $S_3$.
$\mathbb{Q}$ does not have least upper bound property
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real-analysis
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4Please show us what you've thought of so far so that we might be able to guide you through it. Also, please don't ask anything in the imperative - we don't like being told what to do. – 2011-05-12