# Math Help - modulo

1. ## modulo

i was wondering, is l a-b l< lal - lbl?

2. a=3, b=2

3. Or put a = 0, b = 1

4. $\displaystyle (|a-b|)^2\geq (|a|-|b|)^2$

$\displaystyle (|a-b|)^2=(a-b)(a-b)=a^2-2ab+b^2=|a|^2-2ab+|b|^2\geq |a|^2-2|a||b|+|b|^2=(|a|-|b|)^2$

Now take the square root of both sides and we prove the inequality (triangle inequality).

$\displaystyle (|a-b|)^2\geq (|a|-|b|)^2\rightarrow |a-b|\geq |a|-|b|$