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Empty set: Quiz

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Question 1: ________ argued that much of what has been heretofore obtained by set theory can just as easily be obtained by plural quantification over individuals, without reifying sets as singular entities having other entities as members.
George BoolosHilary PutnamMathematical logicGottlob Frege

Question 2: In ________, and more specifically set theory, the empty set is the unique set having no elements; its size is zero.
MathematicsAlgebraMathematical logicGeometry

Question 3: In ________, the existence of the empty set is assured by the axiom of empty set, and its uniqueness follows from the axiom of extensionality.
Zermelo–Fraenkel set theoryZermelo set theoryGeorg CantorClass (set theory)

Question 4: Any statement that begins "for every element of ∅" is not making any substantive claim; it is a ________.
Vacuous truthParaconsistent logicIntuitionistic logicPropositional calculus

Question 5: Its number of elements (that is, its ________) is zero.
CardinalitySet theoryCardinal numberGeorg Cantor

Question 6: The empty set symbol is sometimes used in natural language ________ and morphology to represent morphemes that are not pronounced.
Generative grammarSubject (grammar)GrammarSyntax

Question 7: The latter two symbols were introduced by the Bourbaki group (specifically ________) in 1939, inspired by the letter Ø in the Danish and Norwegian alphabet (and not related in any way to the Greek letter Φ).
Jean-Pierre SerreCarl Ludwig SiegelHenri CartanAndré Weil

Question 8: Null set was once a common synonym for "empty set", but is now a technical term in ________.
Lebesgue integrationLebesgue measureIntegralMeasure (mathematics)

Question 9: Canonical ________ assumes that everything in the (nonempty) domain is a set.
Model theoryGeorg CantorMathematical logicSet theory

Question 10: The empty set can be turned into a ________, called the empty space, in just one way: by defining the empty set to be open.
Compact spaceTopological spaceHausdorff spaceMetric space







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