1. ## Absolute value proofs

Prove the following

1) ||x|-|y|| is less than or equal to |x-y|.

2) If |x-y| < E for all E > 0, then x = y.

2. Originally Posted by noles2188
Prove the following

1) ||x|-|y|| is less than or equal to |x-y|.
see here

2) If |x-y| < E for all E > 0, then x = y.
use the contrapositive.

that is, show that if $x \ne y$, then there is some $\epsilon > 0$ for which $|x - y| \ge \epsilon$

(you need to know the definition of absolute values here)