query: Are all uncountable infinities greater than all countable infinities? Are some uncountable infinities greater than other uncountable infinities?
positive_passages.docid: 27290
positive_passages.text: What Does it Really Mean to Have Different Kinds of Infinities?
negative_passages.docid: 28539
negative_passages.text: Does any uncountable set contain two disjoint uncountable sets?
negative_passages.docid: 87356
negative_passages.text: Are there any known uncountable transfinite increasing sequences of real numbers?
negative_passages.docid: 60678
negative_passages.text: Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
negative_passages.docid: 137564
negative_passages.text: What exactly is meant by infinity?
negative_passages.docid: 134844
negative_passages.text: Summablity and countability
negative_passages.docid: 19777
negative_passages.text: Defining "Countably Infinite"
negative_passages.docid: 156121
negative_passages.text: Existential-universal vs Universal-existential quantifiers
negative_passages.docid: 37991
negative_passages.text: How many different sizes of infinity are there?
negative_passages.docid: 117133
negative_passages.text: Is there an infinite countable $\sigma$-algebra on an uncountable set
negative_passages.docid: 63618
negative_passages.text: Can all ordinals be obtained by taking successors and countable limits?
negative_passages.docid: 112910
negative_passages.text: Is the set of real numbers really uncountably infinite?
negative_passages.docid: 136106
negative_passages.text: Is every open subset of $ \mathbb{R} $ uncountable?
negative_passages.docid: 155168
negative_passages.text: Is the collection of finite subsets of $\mathbb{Z}$ countable?
negative_passages.docid: 144787
negative_passages.text: Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
negative_passages.docid: 2742
negative_passages.text: Is infinity a number?
negative_passages.docid: 3636
negative_passages.text: Are any two uncountable sets similar to each other?