Let u and v be two vectors in RR^2 . The Cauchy-Schwarz inequality states that |u * v| <= |u||v| We are able to transform the above inequality so that it also shows us that |u+v| <= |u|+|v| But I cannot find a way to show that |u−v| <= |u|+|v| even though I now this has to be true. Any ideas?

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