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...as the principle to the effect that in a sum involving [[infinitesimal]]s of different orders, only the lowest-order term must be retained, and the rema | journal = [[Archive for History of Exact Sciences]] ...

...a footnote: "It is interesting that Cauchy does not also mention [[Limit (mathematics)|limits]] here." ...ry]], so that one need never rely on arguments drawn from the [[generality of algebra]]." ...

...within classical mathematics, '''microcontinuity''' (or ''S''-continuity) of an [[internal function]] ''f'' at a point ''a'' is defined as follows: Here ''x'' runs through the domain of ''f''. In formulas, this can be expressed as follows: ...

| subject = [[Mathematics]] ...m of [[Abraham Robinson]] and is sometimes given as '''''An approach using infinitesimals'''''. The book is available freely online and is currently published by Dov ...

...rt.|arxiv=1104.0375 }}</ref> as well as [[Leibniz]]'s [[Transcendental law of homogeneity]]. ...ang: The True History of the Concepts of Limit and Shadow |journal=Notices of the American Mathematical Society |date=1 September 2014 |volume=61 |issue= ...

...d counterexamples |url=https://doi.org/10.1007/BF00934527 |journal=Journal of Optimization Theory and Applications |language=en |volume=39 |issue=2 |page ...nsider a firm which puts safety above all. It wants to maximize the safety of its workers and customers. Subject to attaining the maximum possible safety ...

{{Short description|Historical mathematical concept; form of derivative}} ...of fluxions and infinite series p.20.gif|thumb|400px|Newton's introduction of the notions ''"fluent"'' and ''"fluxion"'' in his 1736 book]] ...

{{Short description|System of numbers with non-finite quantities}} ...s=1795–1815}}</ref> is a [[non-Archimedean ordered field]]; i.e., a system of numbers containing infinite and [[infinitesimal]] quantities. It is usually ...

...toral student of [[Abraham Robinson]], and later a co-author with Robinson of the book ''Nonarchimedean Fields and Asymptotic Expansions''.<ref>''[[Nonar ...tsci/MATHEMATICS_AND_STATISTICS.html Queen's University Academic Calendar, Mathematics and Statistics] {{webarchive |url=https://web.archive.org/web/2010032722475 ...

{{Short description|Type of internal set in nonstandard analysis}} ...te book|title=Truth, possibility, and probability: new logical foundations of probability and statistical inference|url=https://archive.org/details/truth ...

...hose [[kernel (algebra)|kernel]] is the ''R''-module ''M'' (with all pairs of elements in ''M'' having product 0). Note that some authors use '''Exal''' ...of the [[André–Quillen cohomology]] [[group (mathematics)|group]]s and one of the [[Lichtenbaum–Schlessinger functor]]s. ...

...e represents the Cavalieri's Principle in action: if you have the same set of cross sections that only differ by a horizontal translation, you will get t ...y]], '''Cavalieri's principle''', a modern implementation of the '''method of indivisibles''', named after [[Bonaventura Cavalieri]], is as follows:<ref> ...

...At this present time, the article is focused on a 4-dimensional subalgebra of the dual quaternions which will later be called the ''planar quaternions''. ...1.01754|s2cid=2173557 }}</ref><ref>Gunn C. (2011) On the Homogeneous Model of Euclidean Geometry. In: Dorst L., [[Joan Lasenby|Lasenby J.]] (eds) Guide t ...

...\dots</math> and <math>\infty</math> (infinity). That is, it is the result of adding a [[greatest element|maximum element]] <math>\infty</math> to the [[ ...{{sfnp|Escardó|2013}}{{sfnp|Khanjanzadeh|Madanshekaf|2018}} It is a subset of the [[extended real number line]], which extends the [[real number]]s by ad ...

...e]] to the first [[cohomology group]] of the [[sheaf (mathematics)|sheaf]] of [[vector field]]s on&nbsp;''X''. ...g/details/complexmanifolds00koda_517|url-access=limited|series=Classics in Mathematics|year=2005|isbn=978-3-540-22614-7|pages=[https://archive.org/details/complex ...

{{other uses of|differential|topic=mathematics|Differential (mathematics)}} ...[[principal part#Calculus|principal part]] of the change in a [[Function (mathematics)|function]] <math>y = f(x)</math> with respect to changes in the independen ...

{{Distinguish|text=[[Principia Mathematica]]—a book of Russell and Whitehead published in 1910–1913}} | name = The Principles of Mathematics ...

...0/http://control.ee.ethz.ch/~apnoco/Script/15.pdf| url-status=dead}}</ref> of fuzzy logic. ...rudyrucker.com/infinityandthemind/#calibre_link-311 |section=sections 311 "Infinitesimals and Surreal Numbers" and 317 "Random Reals"}}</ref> ...

{{see also|List of numeral systems}} ...ath>): Numbers that can be expressed as a [[fraction (mathematics)|ratio]] of an integer to a non-zero integer.<ref>{{cite web|url=http://mathworld.wolfr ...

| region = [[Mathematics]] ...ranslation of Servois' 1814 Reflections|publisher=Mathematical Association of America|url=http://www.maa.org/sites/default/files/pdf/upload_library/46/Se ...