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Non-standard calculus: Quiz


Question 1: The hyperreals are constructed in the framework of ________, the standard axiomatisation of set theory used elsewhere in mathematics.
Von Neumann–Bernays–Gödel set theoryMorse–Kelley set theorySet theoryZermelo–Fraenkel set theory

Question 2: Here to be precise, f would have to be replaced by its natural hyperreal extension usually denoted f* (see discussion of extension principle in main article at ________).
Hyperreal numberNon-standard calculusNon-standard analysisInfinitesimal

Question 3: In ________, non-standard calculus is the name for the modern application of infinitesimals, in the sense of non-standard analysis, to differential and integral calculus.
MathematicsSet theoryGeometryMathematical logic

Question 4: This fact follows from the ________ of non-standard analysis and overspill.
Hyperreal numberComplex numberReal numberTransfer principle

Question 5: Stripping away the error term, accomplished by an application of the standard part function, was historically considered paradoxical by some writers, most notably ________.
Bertrand RussellGeorge BerkeleyRené DescartesImmanuel Kant

Question 6: As another illustration of the power of Robinson's approach, we present a short proof of the ________ (Bolzano's theorem) using infinitesimals.
Connected spaceReal numberContinuous functionIntermediate value theorem

Question 7: Let i0 be the least element in I (such an element exists by the transfer principle, as I is an internal set; see ________).
Non-standard calculusHyperreal numberNon-standard analysisInfinitesimal

Question 8: This definition has no ________ alternations.The standard (ε, δ)-style definition on the other hand does have quantifier alternations:
AmbiguityFirst-order logicPropositional calculusQuantification


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