query: Comparing the cardinalities of infinite sets
positive_passages.docid: 17987
positive_passages.text: Which of the following sets has the greatest cardinality?(Math subject GRE exam 0568 Q.61 )
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: 97697
negative_passages.text: Countable union of sets of cardinality $c$ has cardinality $c$
negative_passages.docid: 98518
negative_passages.text: Cardinality of equivalence relations on N
negative_passages.docid: 102113
negative_passages.text: Proof that the number of proofs is countably infinite
negative_passages.docid: 272
negative_passages.text: Cantor Sets/nonempty/cardinality
negative_passages.docid: 83518
negative_passages.text: Proving Two sets have same cardinality
negative_passages.docid: 6427
negative_passages.text: how many infinite cardinals are smaller than $\aleph$?
negative_passages.docid: 66398
negative_passages.text: Union of a finite set and a countably infinite set is countably infinite
negative_passages.docid: 81509
negative_passages.text: The cardinality of a countable union of countable sets, without the axiom of choice
negative_passages.docid: 99478
negative_passages.text: countably infinite union of countably infinite sets is countable
negative_passages.docid: 120562
negative_passages.text: If A is an infinite set and B is at most countable set, prove that A and $A \cup B$ have the same cardinality
negative_passages.docid: 102202
negative_passages.text: The smallest infinity and the axiom of choice
negative_passages.docid: 41783
negative_passages.text: Cardinality of the Cartesian Product of Two Equinumerous Infinite Sets
negative_passages.docid: 79974
negative_passages.text: The cardinality of Lebesgue sets
negative_passages.docid: 107614
negative_passages.text: Partitioning an infinite set
negative_passages.docid: 79778
negative_passages.text: $\kappa\cdot\kappa= \kappa,$ for infinite cardinals