A set $X$ is said to be a metric space if and only if there exists $d$:$X \times X \rightarrow \mathbb{R}$ such that
$d(p,p)=0$
$d(p,q)=d(q,p) $
$d(p,q)+d(q,s) \geqq d(p,s)$
$d(p,q)>0 \qquad if \quad p \neq q $
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