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> Let $V$ be an inner product space. Then for all $\vec{u},\vec{v} \in V$ we have $$||\vec{u}-\vec{v}|| \leq ||\vec{u}||+||\vec{v}||.$$
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I know that the converse to the equation is true such that $||\vec{u}+\vec{v}||$ is less than or equal to $||\vec{u}||+||\vec{v}||$. Is this also true?