Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Triangle Inequalities Relationship

  1. Jun 6, 2012 #1
    I know the following
    [tex]|x|-|y| \leq |x+y| \leq |x| + |y|[/tex]
    where does [tex] |x-y| [/tex] fit in the above equation?
     
  2. jcsd
  3. Jun 6, 2012 #2
    How about [itex]x+(-y)[/itex]?

    also, notice that there is a sort of better result, but I like the way you wrote it, makes it easier to remember and figure out what might be needed in a problem. But sometimes the left inequality is written:

    [itex]||x|-|y||\le|x+y|[/itex]

    Just so that you understand when many other people write this.
     
  4. Jun 6, 2012 #3
    So

    [itex]|x|-|y| \leq |x+y| \leq |x| + |y|[/itex]

    and

    [itex]|x|-|y| \leq |x-y| \leq |x| + |y|.[/itex]

    I think we can't say anything about the relationship between[itex]|x+y|[/itex] and [itex]|x-y|,[/itex]
    and in between [itex]||x|-|y|| [/itex]and [itex]|x|-|y|.[/itex]
     
  5. Jun 6, 2012 #4
    [itex]|x+y|\ge||x|-|y||\ge|x|-|y|[/itex]
     
  6. Jun 6, 2012 #5
    You can prove this pretty quickly by plugging numbers in, or just notice that the replacement ##y \mapsto -y## yields the other, hence the only possible relation is equality, which is clearly false.
     
  7. Jun 16, 2012 #6
    if x and y have like signs then lx+yl ≥ lx-yl if unlike signs then lx+yl≤ lx-yl , check it out and always llxl-lyll >= lxl-lyl
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Triangle Inequalities Relationship
  1. Squaring the triangle (Replies: 1)

  2. Triangles in hexagon (Replies: 4)

  3. Linear Relationships (Replies: 2)

Loading...