Proof for reverse triangle inequality $|x - y| \ge |x| - |y|$.

Question

Only step by step hint leading to the final proof.

How should I take it from here?

But suppose the reader is unaware of the final conclusion, how should he begin the proof? — Mathematicing, Apr 06 '15 at 05:15
Can I ascertain that this proof is nothing but algebraic manipulation? I had wanted to know the motivation behind the way the proof was laid out in the outset. — Mathematicing, Apr 06 '15 at 05:24

score 3 · Answer 1 · answered Apr 06 '15 at 05:13

You could divide this up into a lot of cases, and then show it for each case. Why are you forming the cases for $x-y$? Shouldn't you do for $x-y$?

Case 1: $x-y\geq0$
a) $x\geq y\geq0$
b) $x\geq0\geq y$
c) $0\geq x\geq y$

Similarly for Case 2: $x-y<0$

1 Answers1