Question

A proof of the Triangle Inequality for vectors (let v and w be vectors in R^n, then ||v+w||<= ||v||+||w||) WITHOUT using the Cauchy-Schwarz Inequality. Properties of the dot product are okay to use, as are any theorems or definition from prior classes (Calc 3 and prior). This is for a first course in Linear Algebra.

I keep rolling the boulder up the hill only to end up at Cauchy-Schwarz again. Thanks for any help.

Answer 1