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PERSPEX MACHINE IX: TRANSREAL ANALYSIS COPYRIGHT
PERSPEX MACHINE IX: TRANSREAL ANALYSIS COPYRIGHT

... series and their limits, but the existence of an exact nullity is even more profound. The number nullity was shown to lie off the number line by a geometrical construction1 before its arithmetical properties were discovered. When nullity arises in a calculation it means that the formula just evaluat ...
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... is, transitive model of Kripke-Platek set theory) beyond ω1ck . Thus the quantification is really (but implicitly) a bounded universal quantification. (The reason for this pleasantly bounded state of affairs is the Kleene Basis Theorem (see, eg., again Rogers [4], Theorem XLII), which in our contex ...
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Non-standard calculus

In mathematics, non-standard calculus is the modern application of infinitesimals, in the sense of non-standard analysis, to differential and integral calculus. It provides a rigorous justification for some arguments in calculus that were previously considered merely heuristic.Calculations with infinitesimals were widely used before Karl Weierstrass sought to replace them with the (ε, δ)-definition of limit starting in the 1870s. (See history of calculus.) For almost one hundred years thereafter, mathematicians like Richard Courant viewed infinitesimals as being naive and vague or meaningless.Contrary to such views, Abraham Robinson showed in 1960 that infinitesimals are precise, clear, and meaningful, building upon work by Edwin Hewitt and Jerzy Łoś. According to Jerome Keisler, ""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.""
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