Abraham Robinson
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Abraham Robinson was an American mathematician known for his work in mathematical logic and the development of nonstandard analysis. Born in Germany in 1918, Robinson later became an American citizen. His groundbreaking work demonstrated that the concept of infinitesimals, which had been used heuristically in calculus since the time of Newton and Leibniz, was logically consistent.12
Robinson's nonstandard analysis introduced new systems of numbers, including infinitesimals and infinities, that allowed for a rigorous treatment of calculus. This approach, while not widely adopted as the primary method for teaching calculus, offers a powerful alternative perspective on mathematical analysis and has found applications in areas like stochastic differential equations. Robinson passed away in 1974.12
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- Infinitesimals
…the 1960s the German-born American Abraham Robinson similarly used nonstandard models of analysis to create a setting where the nonrigorous infinitesimal arguments of early calculus could be rehabilitated. He found that the old arguments could always be justified, usually with less trouble than the standard justifications with limits. He also…
Read More…the 1960s the German-born American Abraham Robinson similarly used nonstandard models of analysis to create a setting where the nonrigorous infinitesimal arguments of early calculus could be rehabilitated. He found that the old arguments could always be justified, usually with less trouble than the standard justifications with limits. He also…
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analysisNonstandard analysis…work of the German-born mathematician Abraham Robinson in mathematical logic, and it is best described as a variant of real analysis in which infinitesimals and infinities genuinely exist—without any paradoxes. In nonstandard analysis, for example, one can define the limit a of a sequence an to be the unique real…
Read More…work of the German-born mathematician Abraham Robinson in mathematical logic, and it is best described as a variant of real analysis in which infinitesimals and infinities genuinely exist—without any paradoxes. In nonstandard analysis, for example, one can define the limit a of a sequence an to be the unique real…
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