query: Prove that a set has cardinality continuum
positive_passages.docid: 128966
positive_passages.text: Explicit bijection between $\Bbb R$ and permutations of $\Bbb N$
negative_passages.docid: 152382
negative_passages.text: Can an infinite set A be larger than an infinite set B but still have the same cardinality?
negative_passages.docid: 16553
negative_passages.text: Cardinality of the set of all total orders on $\Bbb{N}$
negative_passages.docid: 109070
negative_passages.text: Question about the proof of the distributive property for sets
negative_passages.docid: 88904
negative_passages.text: Help with a proof. Countable sets.
negative_passages.docid: 121366
negative_passages.text: Intervals and cardinality
negative_passages.docid: 89712
negative_passages.text: For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$
negative_passages.docid: 77289
negative_passages.text: Example 2, Sec. 24, in Munkres' TOPOLOGY, 2nd ed: If $X$ is a well ordered set, then $X \times [0, 1)$ is a linear continuum
negative_passages.docid: 92639
negative_passages.text: Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
negative_passages.docid: 41661
negative_passages.text: Show that the set of all finite subsets of $\mathbb{N}$ is countable.
negative_passages.docid: 28391
negative_passages.text: Prove the compactness of a set B
negative_passages.docid: 109968
negative_passages.text: Let $X= \{ A \subset \mathbb{N} : \mathbb{N} \backslash A \text{ is finite}\}$. What is the cardinality of $X$? Prove it.
negative_passages.docid: 85099
negative_passages.text: How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
negative_passages.docid: 14972
negative_passages.text: Cardinality of Vitali sets: countably or uncountably infinite?
negative_passages.docid: 10839
negative_passages.text: Problem in Cardinality and Order
negative_passages.docid: 144735
negative_passages.text: Possible cardinality of power sets
negative_passages.docid: 108922
negative_passages.text: Cardinality and infinite sets: naturals, integers, rationals, bijections