Prove that a metric is always positive.
55016
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
51227
Proving that given metric space is complete: $X := (0,\infty)$ and $d:=|\ln(x)-\ln(y)|$
104339
Prove that all but finite number of members of sequence are positive if limit is positive
21820
How to prove that a set is invariant?
94672
Why is the triangle inequality property important for metric spaces?
105768
Proof involving absolute value and maximums
118353
For set of positive measure $E$, $\alpha \in (0, 1)$, there is interval $I$ such that $m(E \cap I) > \alpha \, m(I)$
17067
To prove that $(\mathbb{P(N)},d)$ is a metric space
83136
Positive Mass Theorem
125899
Prove$ L^2$ inner product satisfies positivity
106698
$\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
14799
How to show that the spherical metric satisfies the triangle inequality?
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
35652
Every compact metric space is complete
69777
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
65491
if the curvature is constant and positive, then it is on the circunference
129163
Showing that every positive integer can be represented in this form