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6h
revised Why do we teach calculus students the derivative as a limit?
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6h
answered Why do we teach calculus students the derivative as a limit?
8h
revised Which universities teach true infinitesimal calculus?
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revised Which universities teach true infinitesimal calculus?
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revised 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
comment 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
revised Which universities teach true infinitesimal calculus?
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Dec
16
awarded  Nice Question
Dec
9
comment Nearest Point to a real algebraic set
In the algebraic case one could try Lagrange multipliers :-)
Dec
8
revised Is non-existence of the hyperreals consistent with ZF?
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Dec
8
comment Is non-existence of the hyperreals consistent with ZF?
@JoelDavidHamkins, good point, thanks.
Dec
8
asked Which universities teach true infinitesimal calculus?
Dec
8
revised Is non-existence of the hyperreals consistent with ZF?
Kanovei-Shelah
Dec
7
comment Is non-existence 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
comment Is non-existence 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
comment Is non-existence 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...