(The triangle inequality: la+bl≤lal+lbl)
The Attempt at a Solution
For the first part, I assumed lxl≥lyl:
Then, by Triangle Inequality
Subtract lyl from both sides to get:
I'm not sure where to go from here. For, llxl-lyll≤lx-yl, don't I need to prove -l(x-y)l≤lxl-lyl≤l(x-y)l? How would I finish the proof?