Results 1 to 4 of 4

Thread: Greatest lower bounds and least upper bounds

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    2

    Exclamation Greatest lower bounds and least upper bounds

    12
    Last edited by mthrcks300; Apr 2nd 2008 at 04:50 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    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 $\displaystyle x$ 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 $\displaystyle A$.
    Last edited by ThePerfectHacker; Mar 31st 2008 at 06:31 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2008
    Posts
    2
    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.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    I made a mistake. Does it make more sense now?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Upper and lower bounds
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Mar 25th 2011, 03:36 AM
  2. Upper and Lower bounds
    Posted in the Math Topics Forum
    Replies: 6
    Last Post: Nov 21st 2010, 05:13 AM
  3. Upper and Lower Bounds
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Sep 4th 2010, 12:04 PM
  4. Upper and Lower Bounds
    Posted in the Algebra Forum
    Replies: 5
    Last Post: Mar 11th 2010, 10:44 AM
  5. Greatest lower bound and lower bounds
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Oct 13th 2009, 02:26 PM

Search Tags


/mathhelpforum @mathhelpforum