Show p(x,y) is a metric on R
65809
Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric
128894
About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
150987
Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
128598
How to prove this is a metric?
136427
Given $∃y.∀x.p(x,y)$, use the Fitch system to prove $∀x.∃y.p(x,y)$
157753
Show that any set in a metric space can be written as the intersection of open sets
135315
Proving whether a function on the set of real sequences is a metric
123039
If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.
72033
Is this proof sufficient to show that a concave function of a metric is also a metric?
110443
Simplifying P(x|y,z) to P(x|z)
132641
Proving that Euclidean Space is a complete metric space
78108
Do these define metrics on $\mathbb{R}$?
70106
diameter on a compact metric space
152196
About inner products, norms and metrics
23203
Euclidean distance proof
49240
$\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$
121359
Show that $d_b(x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric.