i was wondering, is l a-b l< lal - lbl?
$\displaystyle \displaystyle (|a-b|)^2\geq (|a|-|b|)^2$
$\displaystyle \displaystyle (|a-b|)^2=(a-b)(a-b)=a^2-2ab+b^2=|a|^2-2ab+|b|^2\geq |a|^2-2|a||b|+|b|^2=(|a|-|b|)^2$
Now take the square root of both sides and we prove the inequality (triangle inequality).
$\displaystyle \displaystyle (|a-b|)^2\geq (|a|-|b|)^2\rightarrow |a-b|\geq |a|-|b|$