query: The Euclidean metric satisfies triangle inequality in cross product of two metric spaces $X$ and $Y.$
positive_passages.docid: 146485
positive_passages.text: Prove that the product space is a metric space.
negative_passages.docid: 65075
negative_passages.text: norm (x+y)= norm(x-y) implies x is perpendicular to y.
negative_passages.docid: 124688
negative_passages.text: Question about a metric on $\mathbb{R}^2$
negative_passages.docid: 22237
negative_passages.text: Proof of triangle inequality
negative_passages.docid: 150609
negative_passages.text: Triangle Inequality of the Cartesian product with Max function
negative_passages.docid: 27954
negative_passages.text: Prove triangle inequality using the properties of absolute value
negative_passages.docid: 65840
negative_passages.text: Norm induced by metric
negative_passages.docid: 14799
negative_passages.text: How to show that the spherical metric satisfies the triangle inequality?
negative_passages.docid: 157572
negative_passages.text: The distance between two sets inside euclidean space
negative_passages.docid: 3537
negative_passages.text: Show the Euclidean metric and maximum metric are strongly equivalent.
negative_passages.docid: 95901
negative_passages.text: Inequality similar to the Schwarz-Pick theorem
negative_passages.docid: 23203
negative_passages.text: Euclidean distance proof
negative_passages.docid: 128894
negative_passages.text: About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
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: 49087
negative_passages.text: Show that a norm on an inner product space satisfies parallelogram law.
negative_passages.docid: 141643
negative_passages.text: Showing $\rho (x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric
negative_passages.docid: 55016
negative_passages.text: 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