query: Why is $\mathbb Q $ (rational numbers) countable?
positive_passages.docid: 34998
positive_passages.text: How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
negative_passages.docid: 21782
negative_passages.text: Is $\aleph_0 = \mathbb{N}$?
negative_passages.docid: 129109
negative_passages.text: Is the set of polynomial with coefficients on $\mathbb{Q}$ enumerable?
negative_passages.docid: 113892
negative_passages.text: Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
negative_passages.docid: 63276
negative_passages.text: Is an arbitrary union of a chain of countable sets countable?
negative_passages.docid: 16507
negative_passages.text: Is $\mathbb{Z}= \{\dots -3, -2, -1, 0 ,1 ,2 , 3, \dots \}$ countable?
negative_passages.docid: 86893
negative_passages.text: Show that it is impossible to list the rational numbers in increasing order
negative_passages.docid: 23837
negative_passages.text: Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
negative_passages.docid: 33157
negative_passages.text: Proof that an infinite subset of $\mathbb{N}$ is countable
negative_passages.docid: 42810
negative_passages.text: Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
negative_passages.docid: 133266
negative_passages.text: If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis
negative_passages.docid: 76240
negative_passages.text: How is $\epsilon_0$ countable?
negative_passages.docid: 108922
negative_passages.text: Cardinality and infinite sets: naturals, integers, rationals, bijections
negative_passages.docid: 67451
negative_passages.text: Building a bijection from a finite union of countable sets to $\mathbb{N}$
negative_passages.docid: 38549
negative_passages.text: $\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
negative_passages.docid: 128766
negative_passages.text: Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
negative_passages.docid: 77957
negative_passages.text: How is $\mathbb N$ actually defined?