Prove that for any two real numbers a and b $\big||a|-|b|\big|< |a-b|$

Question

I know I should use the triangle inequality.

Can it be done in another way? – grayQuant Jan 25 '14 at 19:26 — grayQuant, Jan 25 '14 at 19:26

score 3 · Answer 1 · answered Jan 25 '14 at 19:24

3

Hint: $|a|=|(a-b)+b|\le|a-b|+|b|$. Then switch the roles of $a$ and $b$.

answered Jan 25 '14 at 19:24

user71352

1 Answers1