query: Equivalence of two dedekind-infinite definitions
positive_passages.docid: 25887
positive_passages.text: Definition of Dedekind-infinity: Bijection or Injections?
negative_passages.docid: 66301
negative_passages.text: The cardinality of the set of countably infinite subsets of an infinite set
negative_passages.docid: 81423
negative_passages.text: Completeness and Topological Equivalence
negative_passages.docid: 62936
negative_passages.text: Proving equivalencies of two versions of the Axiom of Choice
negative_passages.docid: 3902
negative_passages.text: Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
negative_passages.docid: 117561
negative_passages.text: A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
negative_passages.docid: 53707
negative_passages.text: Prove that if $A$ is an infinite set then $A \times 2$ is equipotent to $A$
negative_passages.docid: 79778
negative_passages.text: $\kappa\cdot\kappa= \kappa,$ for infinite cardinals
negative_passages.docid: 49709
negative_passages.text: Suppose $X$ is infinite and $A$ is a finite subset of $X$. Then $X$ and $X \setminus A$ are equinumerous
negative_passages.docid: 76351
negative_passages.text: Equivalence of continuity definitions
negative_passages.docid: 70409
negative_passages.text: Rational Equivalence Relation and Measure
negative_passages.docid: 60678
negative_passages.text: Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
negative_passages.docid: 109054
negative_passages.text: Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
negative_passages.docid: 86926
negative_passages.text: Why isn't this a well ordering of $\{A\subseteq\mathbb N\mid A\text{ is infinite}\}$?
negative_passages.docid: 66398
negative_passages.text: Union of a finite set and a countably infinite set is countably infinite
negative_passages.docid: 140662
negative_passages.text: Powers of infinite cardinals in the generic extension
negative_passages.docid: 69043
negative_passages.text: The equivalence relation generated by a relation