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: Supremum & inifimum

  1. Oct 25, 2007 #1
    I am trying to prove the following. I have a solution below. Can you tell if I am on the right track. P.S. I am doing calculus after 14 yrs so I am very rusty and probably sound stupid

    1- Let T be a non-empty subset of R. Assume T is bounded below. Consider the set S = -T = {-t|t is an element of T}. Show that S is bounded above


    a- Let -a= inf(T)
    b- -(-a) is also an element of S (because it is a mapping)
    c- Let b element of S

    And this is where I am getting stuck at.
    Intuitively, I know that a > b and it will be the supremum in S but I cannot prove it.


  2. jcsd
  3. Oct 25, 2007 #2
    Don't bother with sups and infs if you are trying to give a general upper bound for -T.

    Take the lower bound of T that is assumed to exist, call it B. We know that B<x for all x inside T. What can you say about -B in relation to -x? Now what is the set -T?
  4. Oct 25, 2007 #3
    If B is the lower bound in T and B<x in T
    then -B>-x in all S (as S=-T which is given).

    Is it this simple.
    So in S, would B not be the least upper bound?

    Thanks Siddharth for help

  5. Oct 25, 2007 #4
    B would be supS IF unless of course B=inf(T), in which case -B would be the least upper bound of S (prove it). But above we only assume that B was a lower bound of T not the GREATEST lower bound of T.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook