(1)Prove that for every a, b ∈ R, |a + b| = |a| + |b| ⇐⇒...

(1)Prove that for every a, b ∈ R, |a + b| = |a| + |b| ⇐⇒ ab ≥ 0. Hint: Write |a + b| 2 = (|a| + |b|) 2 and expand.

(2) Prove that for every x, y, z ∈ R, |x − z| = |x − y| + |y − z| ⇐⇒ (x ≤ y ≤ z or z ≤ y ≤ x). Hint: Use part (1) to prove part (2).

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Colby Messinger answered 1 year ago

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