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Interesting questions:
Papers that debunk common myths in the history of mathematics
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Why do we teach calculus students the derivative as a limit?
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answered  Why do we teach calculus students the derivative as a limit? 
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Which universities teach true infinitesimal calculus?
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awarded  Promoter 
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Which universities teach true infinitesimal calculus?
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Which universities teach true infinitesimal calculus?
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Dec 18 
comment 
Which universities teach true infinitesimal calculus?
@Joseph, OK, thanks. 
Dec 18 
revised 
Which universities teach true infinitesimal calculus?
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Dec 18 
comment 
Which universities teach true infinitesimal calculus?
@Joseph, the exposure here is much broader and therefore there is a better chance of getting an answer. 
Dec 18 
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Which universities teach true infinitesimal calculus?
@Willie, this question is similar to other questions under the "teaching" tag, and should be within the scope. 
Dec 18 
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Which universities teach true infinitesimal calculus?
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Dec 16 
awarded  Nice Question 
Dec 9 
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Nearest Point to a real algebraic set
In the algebraic case one could try Lagrange multipliers :) 
Dec 8 
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Is nonexistence of the hyperreals consistent with ZF?
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Dec 8 
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Is nonexistence of the hyperreals consistent with ZF?
@JoelDavidHamkins, good point, thanks. 
Dec 8 
asked  Which universities teach true infinitesimal calculus? 
Dec 8 
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Is nonexistence of the hyperreals consistent with ZF?
KanoveiShelah 
Dec 7 
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Is nonexistence of the hyperreals consistent with ZF?
@EricWofsey, thanks. Note however that a nonprincipal ultrafilter is not enough to prove transfer, so in principle it is possible that in transfer should imply countable additivity, though your comment about Caratheodory does seem to make this difficult. 
Dec 7 
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Is nonexistence of the hyperreals consistent with ZF?
...countable additivity purely from transfer. Apart from Goldblatt's approach, do you think it is feasible to derive countable additivity of Lebesgue measure using hyperfinite subdivisions and transfer? This seems like an interesting question in reverse mathematics where you may be more of an expert than myself (sorry didn't get a chance to look you up on mathscinet yet ;) 
Dec 7 
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Is nonexistence of the hyperreals consistent with ZF?
@EricWofsey, thanks for your comment. I looked over the proof the other day and did not find any mention of countable choice, but perhaps the proof relies on this implicitly. Goldblatt does provide some proofs so you can't make a blanket statement that he constructs them "without proof". It seems to me that the construction of outer measure should be doable without using choice, but I haven't thought about this seriously in a while. Could you substantiate your claims by more specific references to Goldblatt? Reliance on saturation is certainly a difficulty here if one wants to derive... 