Results 1 to 4 of 4

Math Help - Triangle inequality problem

  1. #1
    Member
    Joined
    Mar 2010
    Posts
    175

    Triangle inequality problem

    Can someone show me my mistake. I keep getting |a - b| <= |a| - |b| and it should be the opposite.

    -|a| <= a <= |a|
    -|b| <= b <= |b| //subtract them

    -|a| + b <= a - b <= |a| - |b|
    -(|a| - |b|) <= a - b <= |a| - |b| //therefore

    |a-b| <= |a| - |b|

    Thanks

    (sorry I didn't use latex. I keep getting the math error sign)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1

    Re: Triangle inequality problem

    Quote Originally Posted by jayshizwiz View Post
    Can someone show me my mistake. I keep getting |a - b| <= |a| - |b| and it should be the opposite.

    -|a| <= a <= |a|
    -|b| <= b <= |b| //subtract them

    -|a| + b <= a - b <= |a| - |b|
    -(|a| - |b|) <= a - b <= |a| - |b| //therefore
    |a-b| <= |a| - |b|
    (sorry I didn't use latex. I keep getting the math error sign)
    First: you are using the wrong LaTeX tags.
    [TEX]-|a| \le a \le |a|[/TEX] gives -|a| \le a \le |a|.

    Second: you cannot subtract.
    But, you do know that -|b| \le -b \le |b|.

    Now ADD -(|a|+|b|) \le a-b \le |a|+|b|
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2010
    Posts
    175

    Re: Triangle inequality problem

    what is wrong with subtracting? As long as you don't multiply or divide, it shouldn't affect the sign. Can you possibly give me a counter example.

    Also, I understand what you did with the equation but that's not what I'm trying to prove.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1

    Re: Triangle inequality problem

    Quote Originally Posted by jayshizwiz View Post
    what is wrong with subtracting? As long as you don't multiply or divide, it shouldn't affect the sign. Can you possibly give me a counter example.
    Also, I understand what you did with the equation but that's not what I'm trying to prove.
    From -(|a|+|b|) \le a-b \le |a|+|b| it follows that
    |a-b|\le |a|+|b|.
    Isn't that what you put in the OP?
    If not what are you trying to prove?

    \begin{array}{*{20}c}   {1 \leqslant 2} & {}  \\   { - 1 \leqslant 1} & {}  \\\hline\   {2 \leqslant 1} & {??}  \\\end{array}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Triangle inequality induction problem
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: August 26th 2011, 09:51 AM
  2. Triangle inequality help
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: June 22nd 2011, 03:19 AM
  3. Replies: 3
    Last Post: December 12th 2010, 02:16 PM
  4. Triangle Inequality
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 30th 2009, 11:59 AM
  5. Triangle Inequality Problem
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: January 6th 2009, 11:49 PM

Search Tags


/mathhelpforum @mathhelpforum