1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Prove supS <= infT

  1. Mar 28, 2010 #1
    1. The problem statement, all variables and given/known data
    Let S and T be non-empty subsets of R, and suppose that for all s [tex]\in[/tex] S and t [tex]\in[/tex] T, we have s [tex]\leq[/tex] t.

    Prove that supS [tex]\leq[/tex] infT.

    2. Relevant equations

    3. The attempt at a solution

    Since s [tex]\in[/tex] S [tex]\Rightarrow[/tex] s [tex]\in[/tex] T, supT is an upper bound for S.
    Since supS is the least upper bound, supS [tex]\leq[/tex] supT.

    How does this look to you? Feedback is appreciated.
  2. jcsd
  3. Mar 28, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    [tex]supS \leq supT[/tex] doesn't seem that useful as a start to be honest (supT and infT aren't very close to each other in general). To show that [tex] supS \leq infT[/tex], can you show that infT is an upper bound of S?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook