query: Prove that the Cartesian product of the natural and rational numbers is countably infinite
positive_passages.docid: 27937
positive_passages.text: Cartesian Product of Two Countable Sets is Countable
negative_passages.docid: 84936
negative_passages.text: The set of all finite sequences of members of a countable set is also countable
negative_passages.docid: 9021
negative_passages.text: An infinite subset of a countable set is countable
negative_passages.docid: 68320
negative_passages.text: Infinite Product $\prod\limits_{k=1}^\infty\left({1-\frac{x^2}{k^2\pi^2}}\right)$
negative_passages.docid: 47639
negative_passages.text: Uncountable Cartesian product of closed interval
negative_passages.docid: 139247
negative_passages.text: Real Analysis - Prove a set is countable
negative_passages.docid: 68430
negative_passages.text: Proving the countability of algebraic numbers
negative_passages.docid: 121831
negative_passages.text: Proving that rational numbers are dense
negative_passages.docid: 18223
negative_passages.text: Prove that the union of two disjoint countable sets is countable
negative_passages.docid: 4912
negative_passages.text: Show that an infinite set $C$ is equipotent to its cartesian product $C\times C$
negative_passages.docid: 33157
negative_passages.text: Proof that an infinite subset of $\mathbb{N}$ is countable
negative_passages.docid: 158357
negative_passages.text: Infinite Product $\prod_{n=1}^\infty\left(1+\frac1{\pi^2n^2}\right)$
negative_passages.docid: 55978
negative_passages.text: Prove that for every countable ordinal $\alpha$, $\alpha\times[0,1)$ is order isomoprhic to $[0,1)$
negative_passages.docid: 35692
negative_passages.text: The set of all finite subsets of the natural numbers is countable
negative_passages.docid: 69838
negative_passages.text: Does a countably infinite power set exist?
negative_passages.docid: 67295
negative_passages.text: Please check my proof for $N$ is infinite
negative_passages.docid: 106606
negative_passages.text: How to prove that compact subspaces of the Sorgenfrey line are countable?