Thread: 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)

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 .

Second: you cannot subtract.
But, you do know that .

Now ADD

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.

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 it follows that
.
Isn't that what you put in the OP?
If not what are you trying to prove?