query: For any real t and sequence $|x_n|\rightarrow0$, can always find $k_n \in \mathbb{Z}$ s.t. $k_n |x_n| \to t$?
positive_passages.docid: 144767
positive_passages.text: Picking integers satisfying a limit
negative_passages.docid: 1396
negative_passages.text: cardinality of all real sequences
negative_passages.docid: 108696
negative_passages.text: If $(a_n)_{n\in\mathbb{N}}$ is a Cauchy sequence, then $(a_n ^2)_{n\in\mathbb{N}}$ is also a Cauchy sequence
negative_passages.docid: 153121
negative_passages.text: show that $\{x_n\}$ is a cauchy sequence
negative_passages.docid: 35731
negative_passages.text: Prove that if $A$ is nonsingular, then the sequence $X_{k+1}=X_k+X_k(I-AX_k)$ converges to $A^{-1}$ if and only if $ρ(I-X_0A)<1$.
negative_passages.docid: 119648
negative_passages.text: For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
negative_passages.docid: 51555
negative_passages.text: Strictly increasing sequence $\{ a_k \}$ of positive integers such that $\sum 1/{a_k}$ is finite
negative_passages.docid: 21782
negative_passages.text: Is $\aleph_0 = \mathbb{N}$?
negative_passages.docid: 45788
negative_passages.text: $n$-th digit in the sequence of natural numbers
negative_passages.docid: 71967
negative_passages.text: cardinality of the set of $ \varphi: \mathbb N \to \mathbb N$ such that $\varphi$ is an increasing sequence
negative_passages.docid: 59724
negative_passages.text: Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?
negative_passages.docid: 114123
negative_passages.text: Do the topologies with the same convergent sequences coincide?
negative_passages.docid: 84900
negative_passages.text: Concerning the sequence $\Big(\dfrac {\tan n}{n}\Big) $
negative_passages.docid: 12031
negative_passages.text: Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$
negative_passages.docid: 7645
negative_passages.text: Noetherian property for exact sequence
negative_passages.docid: 129393
negative_passages.text: Product of bounded and convergent to $0$ sequence is a convergent to $0$ sequence
negative_passages.docid: 50934
negative_passages.text: Let $x_n \in[0,1)$ s.t $x_n - \sqrt{n}\in \mathbb{Z}$. Prove that $X=\{x_n | n\in \mathbb{N}\}$ is dense in $[0,1]$.