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- Mar 31st 2008, 04:24 PMmthrcks300Greatest lower bounds and least upper bounds
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- Mar 31st 2008, 04:50 PMThePerfectHacker
I start you off. If $\displaystyle x$ is the greatest lower bound for $\displaystyle B$ then $\displaystyle x\leq b$ for all $\displaystyle b\in B$. But then $\displaystyle x\leq a$ for all $\displaystyle a\in A$ because $\displaystyle A\subseteq B$. This means that $\displaystyle x\leq y$ where $\displaystyle y$ is greatest lower bound for $\displaystyle A$ because $\displaystyle x$ is a lower bound for $\displaystyle A$ and $\displaystyle y$ is

__the greatest__lower bound for $\displaystyle A$. - Mar 31st 2008, 05:27 PMmthrcks300
You start by saying that x is the greatest lower bound for B, but then you say that y is the greatest lower bound for B. I'm confused.

- Mar 31st 2008, 06:31 PMThePerfectHacker
I made a mistake. Does it make more sense now?