Question 1: The hyperreals are constructed in the framework of ________, the standard axiomatisation of set theory used elsewhere in mathematics.  

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 ________).  

Question 3: In ________, nonstandard calculus is the name for the modern application of infinitesimals, in the sense of nonstandard analysis, to differential and integral calculus.  

Question 4: This fact follows from the ________ of nonstandard analysis and overspill.  

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 ________.  

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

Question 7: Let i_{0} be the least element in I (such an element exists by the transfer principle, as I is an internal set; see ________).  

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

