What are the Cauchy sequences in $(X,d)$ when $X = \mathbb{R}$ and d represents the discrete metric?
140379
Cauchy sequence in a discrete space
83790
Why doesn't $d(x_n,x_{n+1})\rightarrow 0$ as $n\rightarrow\infty$ imply ${x_n}$ is Cauchy?
123039
If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.
70746
Proving that $(x_n)_{n=1}^{\infty}$ is a Cauchy sequence.
82458
Homeomorphism between the unit disc and the unit square
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
154694
Is being a Cauchy sequence equivalent to $ \lim_{n\to+\infty}d(x_{n+k},x_n)=0$ for every $k$?
106698
$\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
123828
finite and infinite product of discrete space
100786
Does a continuous function take Cauchy sequences to Cauchy sequences?
121359
Show that $d_b(x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric.
132713
The space $c_0$ of sequences that converge to 0 is not reflexive
46923
Differentiable Sequences
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
22394
Compact operator maps weakly convergent sequences into strongly convergent sequences
150011
Proof completeness of $(X,d)$ given $d$ is French railway metric
51546
Geometrical Interpertation of Cauchy's Mean Value Theorem