query: How do you describe the following set: $\bigcap_{i=0}^{\infty}(\frac{-1}{i}, \frac{1}{i})$
positive_passages.docid: 157336
positive_passages.text: What is the result of $\bigcap_{n=1}^{\infty}{(-1/n; 1/n)}$
negative_passages.docid: 65275
negative_passages.text: Finding $\lim\limits_{x\to1^-}\Bigl(\prod\limits_{n=0}^{\infty}\Bigl(\frac{1+x^{n+1}}{1+x^n}\Bigr)^{x^n}\Bigr)$
negative_passages.docid: 63672
negative_passages.text: Understanding a particular evaluation of $\prod\limits_{n=2}^{\infty}\left(1-\frac{1}{n^3}\right)$
negative_passages.docid: 78471
negative_passages.text: Closure of $\{\frac{1}{n}\}:=M$
negative_passages.docid: 110749
negative_passages.text: Determine $\lim\limits_{n \to \infty}{{n} \choose {\frac{n}{2}}}\frac{1}{2^n}$, where each $n$ is even
negative_passages.docid: 109901
negative_passages.text: Computing $\int_0^\infty\frac1{(x+1)(x+2)\cdots(x+n)}\mathrm dx $
negative_passages.docid: 39034
negative_passages.text: How would you evaluate $\liminf\limits_{n\to\infty} \ n \,|\mathopen{}\sin n|$
negative_passages.docid: 55577
negative_passages.text: Why is $\frac{1}{\infty } \approx 0 $ and $ \frac{1}{0} = {\infty}$?
negative_passages.docid: 68320
negative_passages.text: Infinite Product $\prod\limits_{k=1}^\infty\left({1-\frac{x^2}{k^2\pi^2}}\right)$
negative_passages.docid: 26238
negative_passages.text: What values of alpha guarantee the convergence of $\sum _{n=0}^{\infty }\left( \frac {\alpha n} {n+1}\right) ^{n}$?
negative_passages.docid: 103314
negative_passages.text: Let $\{K_n \}_{n \in \mathbb{N}}$ be a collection of sets, where $K_n = [n, \infty)$. Why is $\bigcap_{n \in \mathbb{N}} K_{n}$ empty?
negative_passages.docid: 147888
negative_passages.text: Show that $M=\bigcap_{\mathfrak{p}\in\operatorname{Spec}(R)}M_\mathfrak{p}=\bigcap_{\mathfrak{m}\in\text{Max}(R)}M_\mathfrak{m}$ for certain $M$.
negative_passages.docid: 56817
negative_passages.text: How do you get \mathbb{1} to work (characteristic function of a set)?
negative_passages.docid: 26211
negative_passages.text: Computing $\lim_{x \to \infty} x \biggl[ \frac{1}{e} - \left( \frac{x}{x+1} \right)^x \biggr]$
negative_passages.docid: 97720
negative_passages.text: Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$
negative_passages.docid: 78008
negative_passages.text: A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$
negative_passages.docid: 108917
negative_passages.text: Use $\delta-\epsilon$ to show that $\lim_{n\to\infty} a^{\frac{1}{n}} = 1$?