query: Show that set of Real numbers has the same cardinality as a set of Irrational Numbers.
positive_passages.docid: 18360
positive_passages.text: Proof that the irrational numbers are uncountable
negative_passages.docid: 96204
negative_passages.text: Irrational number $\sqrt2$ proof
negative_passages.docid: 48797
negative_passages.text: Proving Two Sets are Equal - Infinite Sets - Example
negative_passages.docid: 1396
negative_passages.text: cardinality of all real sequences
negative_passages.docid: 140949
negative_passages.text: Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
negative_passages.docid: 108922
negative_passages.text: Cardinality and infinite sets: naturals, integers, rationals, bijections
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: 30796
negative_passages.text: Is the set of irrationals separable as a subspace of the real line?
negative_passages.docid: 4467
negative_passages.text: Proving Cantor's theorem
negative_passages.docid: 66301
negative_passages.text: The cardinality of the set of countably infinite subsets of an infinite set
negative_passages.docid: 150790
negative_passages.text: Prove two sets have same Cardinality by writing down bijection
negative_passages.docid: 141227
negative_passages.text: How to show the integers have same cardinality as the natural numbers?
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: 149673
negative_passages.text: Cardinality of an infinite union of finite sets
negative_passages.docid: 95947
negative_passages.text: Cantor set + Cantor set =$[0,2]$
negative_passages.docid: 98666
negative_passages.text: Continuity defined for rational and irrational numbers