query: What is the purpose of having obvious axioms in mathematics?
positive_passages.docid: 17480
positive_passages.text: Meaning of the word "axiom"
negative_passages.docid: 154961
negative_passages.text: Are there simple models of Euclid's postulates that violate Pasch's theorem or Pasch's axiom?
negative_passages.docid: 103154
negative_passages.text: Is there a *simple* example of how the axiom of choice can lead to a counterintuitive result?
negative_passages.docid: 5313
negative_passages.text: Existence of how many sets is asserted by the axiom of choice in this case?
negative_passages.docid: 84378
negative_passages.text: Does axiom of foundation/regularity protect against Russell-like paradoxes?
negative_passages.docid: 139866
negative_passages.text: What are the Axiom of Choice and Axiom of Determinacy?
negative_passages.docid: 58447
negative_passages.text: Is axiom of choice required for there to be an infinite linearly independent set in a (non-finite-dimensional) vector space?
negative_passages.docid: 12449
negative_passages.text: How to formulate continuum hypothesis without the axiom of choice?
negative_passages.docid: 157794
negative_passages.text: Are certain fields of physics axiomatized?
negative_passages.docid: 31212
negative_passages.text: The existence of the empty set is an axiom of ZFC or not?
negative_passages.docid: 19138
negative_passages.text: If every object in math can be reduced to sets, how are tuples explained via sets?
negative_passages.docid: 50506
negative_passages.text: What concept does an open set axiomatise?
negative_passages.docid: 58631
negative_passages.text: Continuity and the Axiom of Choice
negative_passages.docid: 42517
negative_passages.text: Is formal truth in mathematical logic a generalization of everyday, intuitive truth?
negative_passages.docid: 105303
negative_passages.text: 'Obvious' theorems that are actually false
negative_passages.docid: 49276
negative_passages.text: Why don't you need the Axiom of Choice when constructing the "inverse" of an injection?
negative_passages.docid: 69337
negative_passages.text: Zorn's Lemma And Axiom of Choice