query: For every infinite cardinal $\kappa$, $\kappa^2 =\kappa$.
positive_passages.docid: 150256
positive_passages.text: About a paper of Zermelo
negative_passages.docid: 127200
negative_passages.text: Are there fields and ordered fields of every infinite cardinality?
negative_passages.docid: 25685
negative_passages.text: What is the product of all nonzero, finite cardinals?
negative_passages.docid: 122814
negative_passages.text: Finite Sets, Equal Cardinality, Injective $\iff$ Surjective.
negative_passages.docid: 70940
negative_passages.text: Homework - set theory infinite union
negative_passages.docid: 158671
negative_passages.text: Cardinality of a set that consists of all existing cardinalities
negative_passages.docid: 69838
negative_passages.text: Does a countably infinite power set exist?
negative_passages.docid: 108957
negative_passages.text: Cardinality of a totally ordered union
negative_passages.docid: 157513
negative_passages.text: How can I prove that these sets are countable infinite?
negative_passages.docid: 9021
negative_passages.text: An infinite subset of a countable set is countable
negative_passages.docid: 117047
negative_passages.text: exponentiation of cardinal number
negative_passages.docid: 23608
negative_passages.text: Prove the set of all infinite binary sequences is uncountable by using Cantor's theorem.
negative_passages.docid: 152382
negative_passages.text: Can an infinite set A be larger than an infinite set B but still have the same cardinality?
negative_passages.docid: 151295
negative_passages.text: Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
negative_passages.docid: 33157
negative_passages.text: Proof that an infinite subset of $\mathbb{N}$ is countable
negative_passages.docid: 1396
negative_passages.text: cardinality of all real sequences
negative_passages.docid: 19777
negative_passages.text: Defining "Countably Infinite"