Nonstandard analysis is a way of doing calculus and analysis with infinitesimals. The historical approach of Leibniz, Euler, and others to infinitesimal calculus was gradually replaced by epsilon, delta techniques in the context of a real continuum, in the 19th century. It was not until the 1960s that Abraham Robinson developed a theory of a hyperreal continuum that allows for a development of analysis procedurally akin to that of its founders.
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A remark of ConnesWas the early calculus inconsistent?
How helpful is non-standard analysis?
Would Euler's proofs get published in a modern math Journal, especially considering his treatment of the Infinite?
Leibnizian calculus textbook
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