query: Cardinality of Natural and positive Rational numbers
positive_passages.docid: 5803
positive_passages.text: Produce an explicit bijection between rationals and naturals?
negative_passages.docid: 48804
negative_passages.text: Enumeration of rationals from Stein-Shakarchi's Real Analysis (Chapter 1, Exercise 24)
negative_passages.docid: 83037
negative_passages.text: Applying Zorn's Lemma to natural numbers
negative_passages.docid: 62687
negative_passages.text: Proving Cardinality of Cosets in Abstract Algebra
negative_passages.docid: 117047
negative_passages.text: exponentiation of cardinal number
negative_passages.docid: 79974
negative_passages.text: The cardinality of Lebesgue sets
negative_passages.docid: 39880
negative_passages.text: Cardinality of Orderings of $\mathbb{R}$
negative_passages.docid: 144735
negative_passages.text: Possible cardinality of power sets
negative_passages.docid: 65768
negative_passages.text: What is the cardinality of the set of the empty set?
negative_passages.docid: 150064
negative_passages.text: Cardinality of "$x-y\in\Bbb Q$"-equivalence class of $1/\sqrt2$
negative_passages.docid: 34998
negative_passages.text: How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
negative_passages.docid: 102972
negative_passages.text: Cardinality of $\mathbb{R}^\mathbb{R}$ by diagonal argument
negative_passages.docid: 149277
negative_passages.text: Does well-ordering of the proper class of cardinal numbers imply choice?
negative_passages.docid: 156660
negative_passages.text: The set of all strictly increasing sequences of natural numbers
negative_passages.docid: 121831
negative_passages.text: Proving that rational numbers are dense
negative_passages.docid: 101028
negative_passages.text: Irrational numbers and Borel Sets
negative_passages.docid: 146436
negative_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?