query: What are some unintuitive consequences if we assume that axiom of choice is wrong?
positive_passages.docid: 86130
positive_passages.text: Which set is unwell-orderable?
negative_passages.docid: 19811
negative_passages.text: $(P(X), C_R)$ may be a choice structure even if $R$ is not a rational relation.
negative_passages.docid: 56191
negative_passages.text: How to demystify the axioms of propositional logic?
negative_passages.docid: 24480
negative_passages.text: Can there be true conclusions without assumptions?
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: 105303
negative_passages.text: 'Obvious' theorems that are actually false
negative_passages.docid: 58631
negative_passages.text: Continuity and the Axiom of Choice
negative_passages.docid: 53025
negative_passages.text: Why the need of Axiom of Countable Choice?
negative_passages.docid: 48030
negative_passages.text: Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem.
negative_passages.docid: 151073
negative_passages.text: What to do with a question that was based on a wrong assumptions?
negative_passages.docid: 139866
negative_passages.text: What are the Axiom of Choice and Axiom of Determinacy?
negative_passages.docid: 13374
negative_passages.text: Why is "the set of all sets" a paradox, in Layman's terms?
negative_passages.docid: 68265
negative_passages.text: Why is it sensical for a proposition with a false antecedent to validate to true?
negative_passages.docid: 12449
negative_passages.text: How to formulate continuum hypothesis without the axiom of choice?
negative_passages.docid: 83757
negative_passages.text: Is the following equivalent to the axiom of choice?
negative_passages.docid: 77654
negative_passages.text: Is the uncertainty principle axiomatic or derived?
negative_passages.docid: 34674
negative_passages.text: Does the proof of Bolzano-Weierstrass theorem require axiom of choice?