(a) Prove the triangle inequality:
||x + y|| ≤ ||x|| + ||y|| for all x, y ∈ ℝn.
(Hint: Use the Cauchy-Schwarz inequality and part 1 of Theorem 2.1.2.)
(b) Show that ||x − y|| ≤ ||x − z|| + ||z − y|| for all x, y, z ∈ ℝn.
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