If I have a $3$ element set, say $X=\{a,b,c\}$ where $d$ is a metric on $X$ with $d(a,b)=5$ and $d(b,c)=7$, then do we have $d(a,c)\in{[0,12]}$ by the triangle inequality? since the distance is greater than or equal to $0$, but less than or equal to the sum of the other $2$ sides.
$$d(a,c)\leq d(a,b)+d(b,c),$$ $$d(a,c)\leq 5+7,$$ $$d(a,c)\leq 12.$$