- #1
Taylor_1989
- 402
- 14
Homework Statement
Hi guys, I would just like someone to go over my method for this derivation/proof ( not sure of the right word to use here). Anyway I think this is right method, but just feel like I am missing something. Could someone please check my method. Thanks in advance.
Homework Equations
$$|x|= x\geq 0 , -x < 0 $$
$$|a-b|\leq|a|-|b|$$
The Attempt at a Solution
By using the formal definition of the absolute value I get this:
[/B]
1.$$-|a|\leq a\leq |a|$$
2.$$-|b|\leq b\leq |b|$$
1-2: $$-(|a|-|b|)\leq a-b \leq |a|-|b| $$
Therefore I get: $$|a-b|\leq|a|-|b|$$
Is this correct? Is there any improvements that anyone could share. I do have a couple more variations of the triangle inequality to go through but want to try the first before posting.