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Non-standard Analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using (ε, δ)-definition of limit, limits rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Nonstandard analysis originated in the early 1960s by the mathematician Abraham Robinson. He wrote: ... the idea of infinitely small or ''infinitesimal'' quantities seems to appeal naturally to our intuition. At any rate, the use of infinitesimals was widespread during the formative stages of the Differential and Integral Calculus. As for the objection ... that the distance between two distinct real numbers cannot be infinitely small, Gottfried Wilhelm Leibniz argued that the theory of infinitesimals implies the introduction of ideal numbers which might be infinitely small or inf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Gottfried Wilhelm Leibniz, Bernhard Christoph Francke
Gottfried is a masculine German given name. It is derived from the Old High German name , recorded since the 7th century, and composed of the elements (conflated from the etyma for "God" and "good", and possibly further conflated with ) and ("peace" or "protection"). The German name was commonly Hypocorism, hypocoristically abbreviated as ''Götz'' from the late medieval period. ''Götz'' and variants (including ''Goethe (surname), Göthe, Göthke'' and ''Göpfert'') also came into use as German surnames. Gottfried is also a common surname among Ashkenazi Jews. Given name The given name ''Gottfried'' became extremely frequent in Germany in the High Middle Ages, to the point of eclipsing most other names in ''God-'' (such as ''Godabert, Gotahard, Godohelm, Godomar, Godwin (other), Goduin, Gotrat, Godulf'', etc.) The name was Latinisation of names, Latinised as ''Godefridus''. Medieval bearers of the name include: *Gotfrid, Duke of Alemannia and Raetia Curiensis, Raetia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |