Proposition 1.3.2. For any two real numbers x, y, we have = |x| |x| = 2 7 7 (b) Prove that for all a R and b 0, we have x|r| (a) Using Proposition 1.3.2 and/or the definition of absolute value, prove that if b = 0, then and |x y| = |x| |y|. |a| |b| = 1 |b|