How to prove that given formula $\frac{(P-Q)^2}{P}+\frac{(P-Q)^2}{Q}$ satisfies triangle inequality ?
2026-05-15 10:20:57.1778840457
How to prove triangle inequality for given formula?
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It doesn't satisfy the triangle inequality. If $d(P,Q)$ is given by your formula, then $$d(1,2)=3/2,\ d(2,3)=5/6,\ d(1,3)=16/3.$$ But $3/2+5/6=7/3<16/3.$