query: Is there a bijection between $\Bbb{R}$ and $\Bbb{R} / \Bbb{Q}$?
positive_passages.docid: 146560
positive_passages.text: Is there any uncountably infinite set that does not generate the reals?
negative_passages.docid: 33014
negative_passages.text: Bijection between an open and a closed interval
negative_passages.docid: 31391
negative_passages.text: bijection between $\mathbb{N}$ and $\mathbb{N}\times\mathbb{N}$
negative_passages.docid: 84114
negative_passages.text: Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
negative_passages.docid: 109764
negative_passages.text: Find the cardinality of the quotient of $\mathbb R$ in respect to R
negative_passages.docid: 128711
negative_passages.text: $(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$?
negative_passages.docid: 79285
negative_passages.text: Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?
negative_passages.docid: 141114
negative_passages.text: Question about a bijection between $\mathbb R$ and $\mathbb R \cup \{\infty\}$
negative_passages.docid: 49833
negative_passages.text: Simple bijection $\mathbb N_0 \times \mathbb N_0 \to \mathbb N_0$
negative_passages.docid: 125894
negative_passages.text: Prove that $\mathbb{Q}$ belongs to the Borel $\sigma$-algebra of $\mathbb{R}$
negative_passages.docid: 19754
negative_passages.text: $\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
negative_passages.docid: 1117
negative_passages.text: Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
negative_passages.docid: 6788
negative_passages.text: Let $(a,b)$ and $(c,d)$ be intervals in $\Bbb R$, and find an injective and surjective function from $(a,b)$ to $(c,d)$
negative_passages.docid: 38257
negative_passages.text: Continuous bijection from $(0,1)$ to $[0,1]$
negative_passages.docid: 85032
negative_passages.text: $Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
negative_passages.docid: 124374
negative_passages.text: A bijective function between a square and its side
negative_passages.docid: 100465
negative_passages.text: Does there exist a continuous bijection from $(-1,1) \to (-1,1]$?