query: Short proof that $\rho^\prime(x,y) = \min\{1,\rho(x,y)\}$ is a metric
positive_passages.docid: 42266
positive_passages.text: Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
negative_passages.docid: 40320
negative_passages.text: Suppose all the Associated Primes are Minimal.
negative_passages.docid: 37953
negative_passages.text: Primary Decomposition of $\mathbb{R^n}$ under T
negative_passages.docid: 12104
negative_passages.text: How to prove this result involving the quotient maps and connectedness?
negative_passages.docid: 73095
negative_passages.text: Foundational proof for Mersenne primes
negative_passages.docid: 128598
negative_passages.text: How to prove this is a metric?
negative_passages.docid: 62950
negative_passages.text: Use implicit function theorem to show $O(n)$ is a manifold
negative_passages.docid: 65809
negative_passages.text: Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric
negative_passages.docid: 152196
negative_passages.text: About inner products, norms and metrics
negative_passages.docid: 123753
negative_passages.text: In a metric $(X,d)$, prove that for each subset $A$, $x\in\bar{A}$ if and only if $d(x,A)=0.$
negative_passages.docid: 9355
negative_passages.text: If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
negative_passages.docid: 9775
negative_passages.text: Metric on Cartesian Product
negative_passages.docid: 23845
negative_passages.text: How to prove the continuity of the metric function?
negative_passages.docid: 6227
negative_passages.text: Showing diffeomorphism between $S^1 \subset \mathbb{R}^2$ and $\mathbb{RP}^1$
negative_passages.docid: 106698
negative_passages.text: $\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
negative_passages.docid: 49503
negative_passages.text: Why does the natural quotient metric works in this case?
negative_passages.docid: 11094
negative_passages.text: How to prove that the French railways metric is a metric