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)
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.