query: problem based on transfinite number concept (Is aleph null itself a set?)
positive_passages.docid: 21782
positive_passages.text: Is $\aleph_0 = \mathbb{N}$?
negative_passages.docid: 45508
negative_passages.text: Is the empty set a group?
negative_passages.docid: 135066
negative_passages.text: How do the authors deduce this weaker version of Transfinite Recursion?
negative_passages.docid: 112910
negative_passages.text: Is the set of real numbers really uncountably infinite?
negative_passages.docid: 109173
negative_passages.text: Why the Sets defined in the Cumulative Hierarchy transitive?
negative_passages.docid: 62197
negative_passages.text: What is $\aleph_0$ powered to $\aleph_0$?
negative_passages.docid: 132692
negative_passages.text: Nonempty set mapped to $\emptyset$ and vice-versa
negative_passages.docid: 59908
negative_passages.text: Intuitive Explanation why the Fundamental Theorem of Algebra fails for infinite sums
negative_passages.docid: 3072
negative_passages.text: If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?
negative_passages.docid: 65467
negative_passages.text: ElGamal in private set intersection: how to handle negative numbers?
negative_passages.docid: 28523
negative_passages.text: When would the intersection of the empty set mean anything?
negative_passages.docid: 110677
negative_passages.text: How is an empty set truly "empty"?
negative_passages.docid: 3663
negative_passages.text: Finding counterexamples in elementary set theory.
negative_passages.docid: 123498
negative_passages.text: Is "empty set" an element of a set?
negative_passages.docid: 118824
negative_passages.text: What is the complement of empty set?
negative_passages.docid: 81250
negative_passages.text: Infinitude of prime numbers
negative_passages.docid: 8082
negative_passages.text: What is A Set Raised to the 0 Power? (In Relation to the Definition of a Nullary Operation)