query: Dependence of Axioms of Equivalence Relation?
positive_passages.docid: 31392
positive_passages.text: Examples and Counterexamples of Relations which Satisfy Certain Properties
negative_passages.docid: 66636
negative_passages.text: Problems with introducing ordered pairs axiomatically
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: 77337
negative_passages.text: Is an Anti-Symmetric Relation also Reflexive?
negative_passages.docid: 85713
negative_passages.text: Showing Parallelism is an equivalence relation in $\Bbb R ^2$
negative_passages.docid: 1704
negative_passages.text: Define a relation and find its equivalence classes.
negative_passages.docid: 130865
negative_passages.text: Why is the axiom of choice separated from the other axioms?
negative_passages.docid: 31389
negative_passages.text: consistency of ZF\{Power Set axiom}
negative_passages.docid: 137921
negative_passages.text: Reflexivity, Transitivity, Symmertry of the square of an relation
negative_passages.docid: 15312
negative_passages.text: Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
negative_passages.docid: 53101
negative_passages.text: Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
negative_passages.docid: 59727
negative_passages.text: Understanding equivalence class, equivalence relation, partition
negative_passages.docid: 157490
negative_passages.text: Statements equivalent to the Axiom of Choice
negative_passages.docid: 83744
negative_passages.text: is there a property of a category that is preserved by category isomorphism, but not equivalence?
negative_passages.docid: 131155
negative_passages.text: $x\sim y\iff x^2\equiv y^2\pmod{\!6}$ is an equivalence relation.
negative_passages.docid: 70409
negative_passages.text: Rational Equivalence Relation and Measure
negative_passages.docid: 153634
negative_passages.text: A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.