query: Get a bounded metric from a metric - triangle inequality for $d'(x,y):=\frac{d(x,y)}{1+d(x,y)}$
positive_passages.docid: 9355
positive_passages.text: If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
negative_passages.docid: 105908
negative_passages.text: Triangle Inequality for SPD Matrix Norm
negative_passages.docid: 88605
negative_passages.text: Proof of the Reverse Triangle Inequality
negative_passages.docid: 42266
negative_passages.text: Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
negative_passages.docid: 15365
negative_passages.text: Proving that the triangle inequality holds for a metric on $\mathbb{C}$
negative_passages.docid: 67253
negative_passages.text: Triangle inequality univalent
negative_passages.docid: 55016
negative_passages.text: Prove that if ($d(x,y)=0$ iff $x=y$) and if $d(x,z)\leq d(x,y)+d(z,y)$ then $d$ is a metric
negative_passages.docid: 135315
negative_passages.text: Proving whether a function on the set of real sequences is a metric
negative_passages.docid: 142414
negative_passages.text: Generalization of metric spaces?
negative_passages.docid: 73469
negative_passages.text: Continuity of the function $x\mapsto d(x,A)$ on a metric space
negative_passages.docid: 49240
negative_passages.text: $\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$
negative_passages.docid: 72033
negative_passages.text: Is this proof sufficient to show that a concave function of a metric is also a metric?
negative_passages.docid: 22237
negative_passages.text: Proof of triangle inequality
negative_passages.docid: 77493
negative_passages.text: Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
negative_passages.docid: 56958
negative_passages.text: bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$
negative_passages.docid: 104217
negative_passages.text: Alternative triangle inequality proof
negative_passages.docid: 74607
negative_passages.text: Variation of the metric with respect to the metric