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Math Help - Greatest lower bounds and least upper bounds

  1. #1
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    Exclamation Greatest lower bounds and least upper bounds

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    Last edited by mthrcks300; April 2nd 2008 at 05:50 AM.
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    Quote Originally Posted by mthrcks300 View Post
    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 x is the greatest lower bound for B then x\leq b for all b\in B. But then x\leq a for all a\in A because A\subseteq B. This means that x\leq y where y is greatest lower bound for A because x is a lower bound for A and y is the greatest lower bound for A.
    Last edited by ThePerfectHacker; March 31st 2008 at 07:31 PM.
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  3. #3
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    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.
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    I made a mistake. Does it make more sense now?
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