query: To show that $X = (0,1]$ is complete with respect to the metric $e $ where $e(x,y) = |\frac{1}{x} - \frac{1}{y}|$.
positive_passages.docid: 16060
positive_passages.text: Showing this metric space is complete
negative_passages.docid: 1641
negative_passages.text: Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
negative_passages.docid: 79040
negative_passages.text: Graph of $|x| + |y| = 1$
negative_passages.docid: 123039
negative_passages.text: If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.
negative_passages.docid: 35573
negative_passages.text: A closed ball in a metric space is a closed set
negative_passages.docid: 130537
negative_passages.text: Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
negative_passages.docid: 104229
negative_passages.text: Show that $\lim\limits_{y\downarrow 0} y\mathbb{E}[\frac{1}{X};X>y]=0$.
negative_passages.docid: 103757
negative_passages.text: how can I prove that $\frac{\arctan x}{x }< 1$?
negative_passages.docid: 69528
negative_passages.text: Metrizability of quotient spaces of metric spaces
negative_passages.docid: 118353
negative_passages.text: For set of positive measure $E$, $\alpha \in (0, 1)$, there is interval $I$ such that $m(E \cap I) > \alpha \, m(I)$
negative_passages.docid: 104413
negative_passages.text: Is the exponential of $-d$ a positive definite kernel for a general metric space $(X, d)$?
negative_passages.docid: 94869
negative_passages.text: Show that $ \int_{k}^{2} \frac{1}{f(y)} =1$
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: 82961
negative_passages.text: Show that $\left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right|$.
negative_passages.docid: 43535
negative_passages.text: show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
negative_passages.docid: 52014
negative_passages.text: Showing $(C[0,1], d_1)$ is not a complete metric space
negative_passages.docid: 101778
negative_passages.text: Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$