query: Prove that (0,1) ⊆ R and (4,10) ⊆ R have the same cardinality
positive_passages.docid: 149382
positive_passages.text: Prove that $(0,1) \subseteq\mathbb R$ and $(4,10) \subseteq\mathbb R$ have the same cardinality.
negative_passages.docid: 13398
negative_passages.text: Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
negative_passages.docid: 113083
negative_passages.text: How to prove a set equality?
negative_passages.docid: 62755
negative_passages.text: The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
negative_passages.docid: 158671
negative_passages.text: Cardinality of a set that consists of all existing cardinalities
negative_passages.docid: 86914
negative_passages.text: Cardinality of the set of hyperreal numbers
negative_passages.docid: 79568
negative_passages.text: Cardinality of the set $D$
negative_passages.docid: 15733
negative_passages.text: Show that the cardinality of $\mathbb N$ is the same as the cardinality of $\mathbb N \times \mathbb N$
negative_passages.docid: 48523
negative_passages.text: Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
negative_passages.docid: 9082
negative_passages.text: Do sets, whose power sets have the same cardinality, have the same cardinality?
negative_passages.docid: 75852
negative_passages.text: Using Pigeonhole Principle to prove two numbers in a subset of $[2n]$ divide each other
negative_passages.docid: 61640
negative_passages.text: Prove c exists for f:[0,1] -> R
negative_passages.docid: 85099
negative_passages.text: How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
negative_passages.docid: 73850
negative_passages.text: Cardinality of set of functions
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: 142267
negative_passages.text: If two sets have the same cardinality, then so do their power sets. Converse can't be answered?
negative_passages.docid: 111954
negative_passages.text: Computing the cardinality of a combinatorial set