query: What does Axiom of Choice mean
positive_passages.docid: 152272
positive_passages.text: Can you explain the "Axiom of choice" in simple terms?
negative_passages.docid: 73368
negative_passages.text: Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?
negative_passages.docid: 98580
negative_passages.text: Lebesgue-measurable sets requiring the Axiom of Choice to construct
negative_passages.docid: 33563
negative_passages.text: Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1)
negative_passages.docid: 12449
negative_passages.text: How to formulate continuum hypothesis without the axiom of choice?
negative_passages.docid: 96026
negative_passages.text: Intuition behind "Exclusive or"
negative_passages.docid: 144899
negative_passages.text: Do We Need the Axiom of Choice for Finite Sets?
negative_passages.docid: 8449
negative_passages.text: Idioms that mean making decision between two good options
negative_passages.docid: 9330
negative_passages.text: Meaning behind Filter in Set Theory
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: 17480
negative_passages.text: Meaning of the word "axiom"
negative_passages.docid: 121847
negative_passages.text: Don't we need the axiom of choice to choose from a non-empty set?
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: 78148
negative_passages.text: Why does the infinite prisoners and hats puzzle require the axiom of choice?
negative_passages.docid: 43503
negative_passages.text: Bases of complex vector spaces and the axiom of choice
negative_passages.docid: 48615
negative_passages.text: Does the assertion that every two cardinalities are comparable imply the axiom of choice?
negative_passages.docid: 126862
negative_passages.text: Confused about $x \notin x$ example in Axiom of Specification