query: Show that if $G$ is a non-trivial subgroup of $\Bbb R$ then either $G$ is dense in $\Bbb R$ or $G=l\Bbb Z$
positive_passages.docid: 26256
positive_passages.text: Characterizing Dense Subgroups of the Reals
negative_passages.docid: 6115
negative_passages.text: Show that $GL_n(\mathbb{F})$ is a finite group iff $\mathbb{F}$ has a finite number of elements
negative_passages.docid: 102912
negative_passages.text: Subgroups of finitely generated groups are not necessarily finitely generated
negative_passages.docid: 25748
negative_passages.text: If $G / Z(G)$ nilpotent then G is nilpotent.
negative_passages.docid: 2761
negative_passages.text: If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
negative_passages.docid: 150337
negative_passages.text: Let $K$ be a subfield of $\mathbb{C}$ not contained in $\mathbb{R}$. Show that $K$ is dense in $\mathbb{C}$.
negative_passages.docid: 12212
negative_passages.text: Showing a certain subspace of Hilbert space is dense
negative_passages.docid: 33387
negative_passages.text: Proof that $n\Bbb Z \leq \Bbb Z$ and are the only subgroups of $\Bbb Z$
negative_passages.docid: 135441
negative_passages.text: When is $\mathbb{Z}[\alpha]$ dense in $\mathbb{C}$?
negative_passages.docid: 45028
negative_passages.text: How to show that $\langle a \rangle$ is a subgroup of a group $G$, where $a$ is in center of the group $G$
negative_passages.docid: 88523
negative_passages.text: Show that $A=\{ \frac{m}{2^n}:m\in \mathbb {Z},n\in \mathbb {N} \} $ is dense in $\mathbb {R}$
negative_passages.docid: 92740
negative_passages.text: prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
negative_passages.docid: 101345
negative_passages.text: Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
negative_passages.docid: 13550
negative_passages.text: For an irrational number $\alpha$, prove that the set $\{a+b\alpha: a,b\in \mathbb{Z}\}$ is dense in $\mathbb R$
negative_passages.docid: 110217
negative_passages.text: $GL(n,K)$ is open in $M(n,K)$
negative_passages.docid: 102622
negative_passages.text: K is a subgroup of G. Show that K is not a normal subgroup
negative_passages.docid: 158018
negative_passages.text: Everywhere Super Dense Subset of $\mathbb{R}$