Turnitin
降AI改写
早检测系统
早降重系统
Turnitin-UK版
万方检测-期刊版
维普编辑部版
Grammarly检测
Paperpass检测
checkpass检测
PaperYY检测
Approaches to analysis with infinitesimals following Robinson, Nelson, and others
This is a survey of several approaches to the framework for working with infinitesimals and
infinite numbers, originally developed by Abraham Robinson in the 1960s, and their …
infinite numbers, originally developed by Abraham Robinson in the 1960s, and their …
Procedures of Leibnizian infinitesimal calculus: An account in three modern frameworks
Recent Leibniz scholarship has sought to gauge which foundational framework provides the
most successful account of the procedures of the Leibnizian calculus (LC). While many …
most successful account of the procedures of the Leibnizian calculus (LC). While many …
Infinitesimal analysis without the Axiom of Choice
It is often claimed that analysis with infinitesimals requires more substantial use of the Axiom
of Choice than traditional elementary analysis. The claim is based on the observation that …
of Choice than traditional elementary analysis. The claim is based on the observation that …
Leibniz on bodies and infinities: rerum natura and mathematical fictions
The way Leibniz applied his philosophy to mathematics has been the subject of
longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an …
longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an …
Infinite lotteries, spinners, applicability of hyperreals
We analyze recent criticisms of the use of hyperreal probabilities as expressed by Pruss,
Easwaran, Parker, and Williamson. We show that the alleged arbitrariness of hyperreal …
Easwaran, Parker, and Williamson. We show that the alleged arbitrariness of hyperreal …
Leibniz's well-founded fictions and their interpretations
Leibniz used the term fiction in conjunction with infinitesimals. What kind of fictions they were
exactly is a subject of scholarly dispute. The position of Bos and Mancosu contrasts with that …
exactly is a subject of scholarly dispute. The position of Bos and Mancosu contrasts with that …
Cauchy's infinitesimals, his sum theorem, and foundational paradigms
Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a
series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and …
series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and …
Bolzano's infinite quantities
In his Foundations of a General Theory of Manifolds, Georg Cantor praised Bernard Bolzano
as a clear defender of actual infinity who had the courage to work with infinite numbers. At …
as a clear defender of actual infinity who had the courage to work with infinite numbers. At …
From Pythagoreans and Weierstrassians to true infinitesimal calculus
In teaching infinitesimal calculus we sought to present basic concepts like continuity and
convergence by comparing and contrasting various definitions, rather than presenting" the …
convergence by comparing and contrasting various definitions, rather than presenting" the …
On mathematical realism and the applicability of hyperreals
We argue that Robinson's hyperreals have just as much claim to applicability as the garden
variety reals. In a recent text, Easwaran and Towsner (ET) analyze the applicability of …
variety reals. In a recent text, Easwaran and Towsner (ET) analyze the applicability of …