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Infinitesimal: Quiz

  

Question 1: The founders of calculus — Euler, Leibniz, Newton, ________, and many others — calculated with infinitesimals and achieved correct results even though no formal definition was available.
Leonhard EulerSiméon Denis PoissonJoseph Louis LagrangeAugustin-Louis Cauchy

Question 2: For example, there would have to be a ________ function that was well defined for infinite inputs.
TrigonometryGenerating trigonometric tablesPythagorean theoremTrigonometric functions

Question 3: ________, in The Method of Mechanical Theorems, was the first to propose a logically rigorous definition of infinitesimals.
EuclidDemocritusThalesArchimedes

Question 4: The extended axioms are IST, which stands either for ________ or for the initials of the three extra axioms: Idealization, Standardization, Transfer.
Non-standard analysisReal numberConsistencyInternal set theory

Question 5: A ________ has all the first-order properties of the real number system (regardless of whether they are usually taken as axiomatic) for statements involving the basic ordered-field relations +, ×, and ≤.
Field (mathematics)Ordered fieldHyperreal numberReal closed field

Question 6: The word infinitesimal comes from a 17th century ________ coinage infinitesimus, which originally referred to the "infinite-th" item in a series.
New LatinContemporary LatinVulgar LatinRenaissance Latin

Question 7: For example, the ________ axiom x + y = y +  x holds.
CommutativityGroup (mathematics)Vector spaceRing (mathematics)

Question 8: As an alternative to infinitesimals, the ________ in the 14th to 16th centuries made use of an intuitive notion of a limit to compute several series expansions.
Indian mathematicsMadhava of SangamagramaNilakantha SomayajiKerala school of astronomy and mathematics

Question 9: [1] His ________ defines a number x as infinite if it satisfies the conditions |x|>1, |x|>1+1, |x|>1+1+1, ..., and infinitesimal if x≠0 and the same set of conditions holds for 1/x.
Algebraic structureReal numberArchimedean propertyField (mathematics)

Question 10: For comparison one should note that there was no formal definition of ________ at the time, either.
Complex numberIrrational numberReal numberTranscendental number
















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