# Math Help - Triangle inequality problem

1. ## 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)

2. ## Re: Triangle inequality problem

Originally Posted by jayshizwiz
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 $-(|a|+|b|) \le a-b \le |a|+|b|$

3. ## 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.

4. ## Re: Triangle inequality problem

Originally Posted by jayshizwiz
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?

$\begin{array}{*{20}c} {1 \leqslant 2} & {} \\ { - 1 \leqslant 1} & {} \\\hline\ {2 \leqslant 1} & {??} \\\end{array}$