Proving that $\rho(x,y) = \frac{d(x,y)}{1+d(x,y)}$ is a metric and that $\rho(x,y)$ and $d(x,y)$ are equivalent metrics
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
128764
How does $y[x] = a x^r$ when $y'[x] = \frac{(r y[x])}{x}$ and $y[1] = a$
3751
Proving a distance between molecules defines a metric space.
135059
Prove that the unit circle, $S^1:=\{(x,y)\in \mathbb{R}^2: x^2+y^2=1\}$, Is a one-dimensional manifold
17067
To prove that $(\mathbb{P(N)},d)$ is a metric space
77270
Find the correlation coefficient $\rho_g$ of $(G(x), H(y))$
132641
Proving that Euclidean Space is a complete metric space
23845
How to prove the continuity of the metric function?
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
11094
How to prove that the French railways metric is a metric
157155
How is HCF (c, d) = HCF (d, r), where c = dq +r (by Euclid's division lemma)?
114047
Metric $d(x,y)=\frac{|x-y|}{\sqrt{1+x^2}\sqrt{1+y^2}}$ on $\mathbb{R}$
132528
Are metrics that determine the same topology, equivalent?
86193
Rigorous proof that $dx dy=r\ dr\ d\theta$
23203
Euclidean distance proof
121359
Show that $d_b(x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric.
94218
Showing $d(x,y) = \frac{|x-y|}{1+|x-y|}$ is a distance.