1. Not finding help here? Sign up for a free 30min 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!

Absolute inequalities

  1. Sep 27, 2004 #1
    prove the folowing and state when the inequality holds...

    |x+y+z|<=|x|+|y|+|z|

    i was thinking that i consider all the possible cases, ie x is positive, y positive, z positive; then the various combinations with negative as well.....
    is there another shorter method of doing it?
    help.....
     
  2. jcsd
  3. Sep 27, 2004 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    You can start with 2 terms first. |x+y|<=|x|+|y|. (I am assuming you are talking about real numbers). Equal if the same sign, less if opposite. Then the 3 term case can be proven in two steps using the 2 term case.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Absolute inequalities
Loading...