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High Quality Content by WIKIPEDIA articles! In mathematics, non-standard calculus is the name for the modern application of infinitesimals, in the sense of non-standard analysis, to differential and integral calculus. It provides a rigorous justification of what were previously believed to be purely formal calculations. Calculations with infinitesimals were widely used before the theory of limits replaced them in the 19th century. See history of calculus. To quote H. Jerome Keisler: "In [1960], Robinson solved a three hundred year old problem by giving a precise treatment of infinitesimals. Robinson's achievement will probably rank as one of the major mathematical advances of the twentieth century"