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Mar
26
comment Has anybody ever considered “full derivative”?
@Mark S. what a problem in defining $\sin \varepsilon$? It just can be represented as a series or in closed form... Where the problem is?
Mar
25
revised Has anybody ever considered “full derivative”?
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Mar
25
comment Has anybody ever considered “full derivative”?
@Kevin Carlson is this field truly hyperreal?
Mar
25
revised Has anybody ever considered “full derivative”?
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Mar
25
comment Has anybody ever considered “full derivative”?
@Mark S. so basically if to add to rationals $\varepsilon$ as in this post we get Levi-Civita field?
Mar
25
comment Why hyperreal numbers are built so complicatedly?
What questions about calculus remain unanswered?
Mar
25
comment Has anybody ever considered “full derivative”?
@Mark S. $No(\omega)$ is a hyperreal system, subfield of surreals ohio.edu/people/ehrlich/Unification.pdf
Mar
25
revised Has anybody ever considered “full derivative”?
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Mar
25
revised Has anybody ever considered “full derivative”?
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Mar
25
awarded  Nice Question
Mar
25
comment Has anybody ever considered “full derivative”?
@Hayden I am about introducing one element, $\varepsilon$, similarly to how complex $i$ introduced. One can argue such system would be undefinable, but then complex numbers are also undefinable because $i$ is indistinguishable from $-i$. By the way, in the context of surreals, hyperreal numbers can be considered a subfield $No(\omega)$. Then this $\omega$ has definite meaning: it is considered equal to the first infinite ordinal.
Mar
25
revised General form for series coefficient of Taylor series expansion of $(x+1)^{1/x}$
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Mar
25
comment General form for series coefficient of Taylor series expansion of $(x+1)^{1/x}$
@mickep around zero
Mar
25
revised Has anybody ever considered “full derivative”?
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Mar
25
revised Has anybody ever considered “full derivative”?
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Mar
25
asked General form for series coefficient of Taylor series expansion of $(x+1)^{1/x}$
Mar
25
revised Has anybody ever considered “full derivative”?
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Mar
25
comment Has anybody ever considered “full derivative”?
@Hayden in usual non-standard analysis they usually do not introduce distinguished elements $\varepsilon$ and $\omega$, thus they cannot uniquely define full derivative.
Mar
25
revised Has anybody ever considered “full derivative”?
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Mar
25
revised Has anybody ever considered “full derivative”?
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