query: How to prove that every regular ordinal is a cardinal?
positive_passages.docid: 21479
positive_passages.text: Why cofinality is a cardinal.
negative_passages.docid: 145397
negative_passages.text: How to prove that for every $i$, $a_i = i$
negative_passages.docid: 16971
negative_passages.text: Prove that no ordinal is an element of itself
negative_passages.docid: 4467
negative_passages.text: Proving Cantor's theorem
negative_passages.docid: 49440
negative_passages.text: Prove that the interval $ \ [0,2)$ and $ \ [5,6) \cup [7,8)$ have the same cardinality
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: 12436
negative_passages.text: The cardinality of the set of all finite subsets of an infinite set
negative_passages.docid: 98163
negative_passages.text: Question regarding exponentiation of cardinal numbers
negative_passages.docid: 121366
negative_passages.text: Intervals and cardinality
negative_passages.docid: 153652
negative_passages.text: Countable ordinals are embeddable in the rationals $\Bbb Q$ -- proofs and their use of AC
negative_passages.docid: 63618
negative_passages.text: Can all ordinals be obtained by taking successors and countable limits?
negative_passages.docid: 36325
negative_passages.text: Embedding ordinals in $\mathbb{Q}$
negative_passages.docid: 15438
negative_passages.text: do all uncountable sets have same cardinality as real numbers?
negative_passages.docid: 20085
negative_passages.text: What's the cardinality of all sequences with coefficients in an infinite set?
negative_passages.docid: 1396
negative_passages.text: cardinality of all real sequences
negative_passages.docid: 122947
negative_passages.text: What is the cardinality of the set of infinite cardinalities?
negative_passages.docid: 138283
negative_passages.text: $|(a,b)| = |\Bbb R|$ ? Cardinality of any open interval