query: Prove that a subgroup is dense in $\mathbb{R}$
positive_passages.docid: 151210
positive_passages.text: How can we find and categorize the subgroups of $\mathbb{R}$?
negative_passages.docid: 113614
negative_passages.text: Approximating the density of $S\cap[a,b]$ using a Folner Sequence of $A$, where $S \subseteq A$?
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: 140052
negative_passages.text: Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
negative_passages.docid: 74498
negative_passages.text: Smallest dense subset of $\mathbb{R}$
negative_passages.docid: 27670
negative_passages.text: Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
negative_passages.docid: 78580
negative_passages.text: Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
negative_passages.docid: 14048
negative_passages.text: Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
negative_passages.docid: 129753
negative_passages.text: Prove that a subgroup which contains half of all elements is a normal subgroup.
negative_passages.docid: 10602
negative_passages.text: Monotone Union of subgroups being subgroup
negative_passages.docid: 90590
negative_passages.text: Prove that the following set is dense
negative_passages.docid: 42891
negative_passages.text: Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
negative_passages.docid: 78915
negative_passages.text: Density of the set $S=\{m/2^n| n\in\mathbb{N}, m\in\mathbb{Z}\}$ on $\mathbb{R}$?
negative_passages.docid: 92740
negative_passages.text: prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
negative_passages.docid: 142228
negative_passages.text: Proof that a subset closed under group operation of a finite group is a subgroup
negative_passages.docid: 106434
negative_passages.text: Prove that for a dense set $A$ and an open set $U$, $U\subset \overline{A\cap U}$
negative_passages.docid: 98542
negative_passages.text: Prove that $H$ is a subgroup of an abelian group $G$