query: $\mathbb{R}^3$ \ $\mathbb{Q}^3$ is a union of disjoint lines, The lines are not in an axis direction.
positive_passages.docid: 25854
positive_passages.text: $\mathbb{R}^3$ \ $\mathbb{Q}^3$ is union of disjoint lines. The lines are not in an axis diretion.
negative_passages.docid: 46917
negative_passages.text: How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
negative_passages.docid: 78006
negative_passages.text: What is known about the quotient group $\mathbb{R} / \mathbb{Q}$?
negative_passages.docid: 84148
negative_passages.text: Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$?
negative_passages.docid: 88051
negative_passages.text: $\mathbb R = X^2$ as a Cartesian product
negative_passages.docid: 61962
negative_passages.text: Show $R$ is right-Artinian but not left-Artinian
negative_passages.docid: 108550
negative_passages.text: Elements of $\mathbb Q(2^{1/3})$
negative_passages.docid: 96354
negative_passages.text: Linear independence of $\sin(x)$, $\sin(2x)$, $\sin(3x)$ in Map($\mathbb{R},\mathbb{R}$)
negative_passages.docid: 78873
negative_passages.text: How to show that the monomials are not a Schauder basis for $C[0,1]$
negative_passages.docid: 157597
negative_passages.text: Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
negative_passages.docid: 114987
negative_passages.text: How many connected components does $\mathrm{GL}_n(\mathbb R)$ have?
negative_passages.docid: 134294
negative_passages.text: A (not necessarily unitary) $R$ module $M$ splits into $B\oplus C$ where $B$ is unitary and $RC=\{0\}$.
negative_passages.docid: 68838
negative_passages.text: Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?
negative_passages.docid: 95221
negative_passages.text: Is the cuspidal cubic $\{y^2 = x^3\} \subset \Bbb R^2$ not smooth?
negative_passages.docid: 30231
negative_passages.text: The boundary of union is the union of boundaries when the sets have disjoint closures
negative_passages.docid: 88474
negative_passages.text: $\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
negative_passages.docid: 26764
negative_passages.text: Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)