query: Show that $\mathbb{Q}\times \mathbb{Q}$ is denumerable
positive_passages.docid: 54406
positive_passages.text: Is $\mathbb Q \times \mathbb Q $ a denumerable set?
negative_passages.docid: 137201
negative_passages.text: Classifying $\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z} / \langle(3,3,3)\rangle$
negative_passages.docid: 152297
negative_passages.text: Understanding quotients of $\mathbb{Q}[x]$
negative_passages.docid: 762
negative_passages.text: Proving every infinite set $S$ contains a denumerable subset
negative_passages.docid: 111348
negative_passages.text: Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$
negative_passages.docid: 109219
negative_passages.text: How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?
negative_passages.docid: 129109
negative_passages.text: Is the set of polynomial with coefficients on $\mathbb{Q}$ enumerable?
negative_passages.docid: 120035
negative_passages.text: Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
negative_passages.docid: 3296
negative_passages.text: Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
negative_passages.docid: 87848
negative_passages.text: Formal proof for $(-1) \times (-1) = 1$
negative_passages.docid: 118299
negative_passages.text: Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
negative_passages.docid: 38364
negative_passages.text: Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
negative_passages.docid: 45991
negative_passages.text: Why $f\colon \mathbb{Z}_n^\times \to \mathbb{Z}_m^\times$ is surjective?
negative_passages.docid: 41035
negative_passages.text: Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
negative_passages.docid: 64130
negative_passages.text: Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
negative_passages.docid: 132311
negative_passages.text: T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$
negative_passages.docid: 35626
negative_passages.text: Is $(\mathbb{R}^2, lexicographic) \cong (\mathbb{R}, discrete)\times (\mathbb{R}, usual)$?