Prove that, if $d$ is a metric, then $\frac{d}{1+d}$ is equivalent to $d$.
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
34362
Are there any examples of $\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$?
72033
Is this proof sufficient to show that a concave function of a metric is also a metric?
91285
Prove $a+b+c+d $ is composite
85242
Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
81794
Prove that $(ab,cd)=(a,c)(b,d)\left(\frac{a}{(a,c)},\frac{d}{(b,d)}\right)\left(\frac{c}{(a,c)},\frac{b}{(b,d)}\right)$
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
91000
Prove that $\frac{1}{a+1}0$
119105
If $(X,d)$ is a complete metric space and $A$ is closed then show that for $x \in X$ there exists an element $a_0 \in A$ such that $d(x,A)=d(x,a_0)$
3537
Show the Euclidean metric and maximum metric are strongly equivalent.
17241
How to prove $ \prod_{d|n} d= n^{\frac{\tau (n)}{2}}$
9696
The interval [0,1] andd [3,5] are equivalent. Is my proof correct?
51227
Proving that given metric space is complete: $X := (0,\infty)$ and $d:=|\ln(x)-\ln(y)|$
123061
$X$ metric separable then $C(X)$ separable
27652
metric on the Euclidean Group
52565
Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.
127034
Let $\rho(x,y)= \frac{d(x,y)}{1+d(x,y)}$, show that $\rho$ is a metric equivalent to $d$