Thread: 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.

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 , then there is some for which

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