query: $\vert \mathbb{R}^{\mathbb{Z}} \vert = \vert \mathbb{R} \vert $?
positive_passages.docid: 1396
positive_passages.text: cardinality of all real sequences
negative_passages.docid: 76971
negative_passages.text: Entire functions bounded along $\vert z\vert = R$
negative_passages.docid: 155745
negative_passages.text: Ideals of $\mathbb{Z}[X]$
negative_passages.docid: 118073
negative_passages.text: Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
negative_passages.docid: 16559
negative_passages.text: Difference between $\mathbb{Z}/n\mathbb{Z}$ and $\mathbb{Z}_n$
negative_passages.docid: 116943
negative_passages.text: Proof for maximal ideals in $\mathbb{Z}[x]$
negative_passages.docid: 145879
negative_passages.text: $R$ is PID, so $R/I$ is PID, and application on $\mathbb{Z}$ and $\mathbb{N}$
negative_passages.docid: 144105
negative_passages.text: Ring homomorphism from $\mathbb Z$ to $\mathbb Z$ is always identity or $0$
negative_passages.docid: 139934
negative_passages.text: In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?
negative_passages.docid: 97258
negative_passages.text: Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$
negative_passages.docid: 92211
negative_passages.text: When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
negative_passages.docid: 15909
negative_passages.text: Bijection from $\mathbb R$ to $\mathbb {R^N}$
negative_passages.docid: 27188
negative_passages.text: Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
negative_passages.docid: 51695
negative_passages.text: Finding all homomorphisms between $\mathbb{Z}/m\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 61375
negative_passages.text: Meaning of $\mathbb{R}[x]$
negative_passages.docid: 35777
negative_passages.text: $\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
negative_passages.docid: 153204
negative_passages.text: Euclidean domain $\mathbb{Z}[\sqrt{d}]$