query: Prove that $n+2$ points in $\Bbb R^n$ cannot all be at a unit distance from each other.
positive_passages.docid: 23596
positive_passages.text: Proof maximum number of equidistant points for a given dimension
negative_passages.docid: 82474
negative_passages.text: Isometries of $\mathbb{R}^n$
negative_passages.docid: 108909
negative_passages.text: Is the unit sphere in $\Bbb R^4$ path connected?
negative_passages.docid: 64523
negative_passages.text: interior points and limit points of $\{(x,y): x^2+2y^2 < 1\}$
negative_passages.docid: 96845
negative_passages.text: Question: Compare the cardinality between the sets $\Bbb R$ and $\Bbb N^{\Bbb N}$
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: 156671
negative_passages.text: Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
negative_passages.docid: 24585
negative_passages.text: Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
negative_passages.docid: 56728
negative_passages.text: Question about limit points of a Subset of $\mathbb{R}$
negative_passages.docid: 101176
negative_passages.text: Suppose that $(s_n)$ converges to s. Prove that $(s_n^2)$ converges to $s^2$
negative_passages.docid: 4776
negative_passages.text: Prove that the power set of an $n$-element set contains $2^n$ elements
negative_passages.docid: 6491
negative_passages.text: Not every open set in $\mathbb{R}^n$, for $n\geq2$, is a disjoint union of countable open balls.
negative_passages.docid: 158534
negative_passages.text: Proof that any linear system cannot have exactly 2 solutions.
negative_passages.docid: 36878
negative_passages.text: Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.
negative_passages.docid: 66272
negative_passages.text: Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
negative_passages.docid: 131754
negative_passages.text: Prove $ \forall c \in \mathbb{R^{+}}, \forall B \in \mathbb{N}, \exists n \in \mathbb{N}, (n \geq B) \wedge (\sqrt{2n} > c \ln(n+2)) $?
negative_passages.docid: 32772
negative_passages.text: Proving units in a ring