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Math · Advanced Math
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Let \small N be a norm on a linear space \small V and let \small d be defined for \small u, v\in V by \small d(u,v) = N(u-v) . Show that \small d is a metric on \small N; that is,

i) \small d(u, v)\geq 0 for all \small u, v \in V

ii) \small d(u, v)\ = 0 if and only if \small u = v

iii) \small d(u,v) = d(v, u)

iv) \small d(u,v) \leq d(u, w) + d(w, v)

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