The definition of a metric and the triangle inequality
94672
Why is the triangle inequality property important for metric spaces?
1316
Reverse Triangle Inequality in vector space
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
49503
Why does the natural quotient metric works in this case?
124688
Question about a metric on $\mathbb{R}^2$
72950
Book recommendation for Metric Spaces
36758
Triangle inequality for L2 norm
106816
Medians of a triangle and similar triangle properties
146485
Prove that the product space is a metric space.
26299
Minkowski Metric Signature
132641
Proving that Euclidean Space is a complete metric space
129161
The minimum perimeter and maximum height of a triangle under constraints
3751
Proving a distance between molecules defines a metric space.
106698
$\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
54685
Defining metrics as a function to something other than the reals.
123753
In a metric $(X,d)$, prove that for each subset $A$, $x\in\bar{A}$ if and only if $d(x,A)=0.$
93599
General Proof for the triangle inequality