query: Proving density of $\mathbb{Q}^n$ in $\mathbb{R}^n$
positive_passages.docid: 25795
positive_passages.text: Density of $\mathbb{Q}^n$ in $\mathbb{R}^n$
negative_passages.docid: 120522
negative_passages.text: Showing any countable, dense, linear ordering is isomorphic to a subset of $\mathbb{Q}$
negative_passages.docid: 142577
negative_passages.text: Algebraic proof that a set generated by irrational rotations is dense in $S^1$.
negative_passages.docid: 6523
negative_passages.text: Prove that the space has a countable dense subset
negative_passages.docid: 57839
negative_passages.text: Real analysis: density and continuity
negative_passages.docid: 106625
negative_passages.text: Strength of the statement "$\mathbb R$ has a Hamel basis over $\mathbb Q$"
negative_passages.docid: 158011
negative_passages.text: $C_c^{\infty}(\mathbb R^n)$ is dense in $W^{k,p}(\mathbb R^n)$
negative_passages.docid: 152451
negative_passages.text: REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
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: 82474
negative_passages.text: Isometries of $\mathbb{R}^n$
negative_passages.docid: 61103
negative_passages.text: Prove that $\mathbb{|Q| = |Q\times Q|}$
negative_passages.docid: 154076
negative_passages.text: How to show this property of $\mathbb{RP}^{n}$.
negative_passages.docid: 17461
negative_passages.text: Show that a set is dense in $[-1,1]$
negative_passages.docid: 135772
negative_passages.text: how to show image of a non constant entire function is dense in $\mathbb{C}$?
negative_passages.docid: 75829
negative_passages.text: Dimension of open subsets of $R^n$
negative_passages.docid: 36747
negative_passages.text: $\text{Tor}_0^R(M,N)\simeq M\otimes_R N$
negative_passages.docid: 143067
negative_passages.text: Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.