1. The problem statement, all variables and given/known data Prove llxl-lyll≤lx-yl (The triangle inequality: la+bl≤lal+lbl) 3. The attempt at a solution For the first part, I assumed lxl≥lyl: lxl=l(x-y)+yl Then, by Triangle Inequality l(x+y)+yl≤l(x-y)l+lyl So, lxl≤l(x-y)l+lyl Subtract lyl from both sides to get: lxl-lyl≤l(x-y)l. 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? Thank you.