infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Nonstandard analysis originated...

In mathematics, constructive nonstandard analysis is a version of Abraham Robinson's nonstandard analysis, developed by Moerdijk (1995), Palmgren (1998)...

In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics. The name of the subject contrasts...

In mathematics, nonstandard calculus is the modern application of infinitesimals, in the sense of nonstandard analysis, to infinitesimal calculus. It provides...

Nonstandard analysis and its offshoot, nonstandard calculus, have been criticized by several authors, notably Errett Bishop, Paul Halmos, and Alain Connes...

In nonstandard analysis, a monad or also a halo is the set of points infinitesimally close to a given point. Given a hyperreal number x in R∗, the monad...

portal Constructive nonstandard analysis Hyperinteger – A hyperreal number that is equal to its own integer part Influence of nonstandard analysis Nonstandard...

In nonstandard analysis, a hyperinteger n is a hyperreal number that is equal to its own integer part. A hyperinteger may be either finite or infinite...

approach to nonstandard analysis (see also Palmgren at constructive nonstandard analysis). Conventional infinitary accounts of nonstandard analysis also use...

other branches of mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus. He also introduced much of modern mathematical...

popularity in the 20th century with Abraham Robinson's development of nonstandard analysis and the hyperreal numbers, which, after centuries of controversy...

was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite...

Synthetic differential geometry Smooth infinitesimal analysis Constructive nonstandard analysis Infinitesimal strain theory (physics) Formalizations Differentials...

219–318, doi:10.1016/j.hm.2010.07.001 Arkeryd, Leif (Dec 2005), "Nonstandard Analysis", The American Mathematical Monthly, 112 (10): 926–928, doi:10.2307/30037635...

et analysi indivisibilium atque infinitorum" (On a hidden geometry and analysis of indivisibles and infinites), published in Acta Eruditorum in June 1686...

Application of Dual Algebra to Kinematic Analysis", Computational Methods in Mechanical Systems: Mechanism Analysis, Synthesis, and Optimization, NATO ASI...

In nonstandard analysis, a branch of mathematics, overspill (referred to as overflow by Goldblatt (1998, p. 129)) is a widely used proof technique. It...

construction of the real numbers differs from the Dedekind cuts of standard analysis in that it starts from dyadic fractions rather than general rationals and...

infinitesimals and infinitely large numbers. This is the approach of nonstandard analysis pioneered by Abraham Robinson. These approaches are very different...

coefficients be complex. It is rich enough to allow a significant amount of analysis to be done, but its elements can still be represented on a computer in...

Reformulations of calculus in a constructive framework are generally part of the subject of constructive analysis. While many of the ideas of calculus...

hyperreal number system. Its most common use is in Abraham Robinson's nonstandard analysis of the hyperreal numbers, where the transfer principle states that...

as a subfield, are used to provide a mathematical foundation for nonstandard analysis. Max Dehn used the Dehn field, an example of a non-Archimedean ordered...

In nonstandard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers. Briefly, the standard...

the key theorems of calculus (thereby creating real analysis), pioneered the field complex analysis, and the study of permutation groups in abstract algebra...

achievement was in the theory of numbers." Regarding Fermat's work in analysis, Isaac Newton wrote that his own early ideas about calculus came directly...

ideology, and the politics of infinitesimals: mathematical logic and nonstandard analysis in modern China". History and Philosophy of Logic. 24 (4): 327–363...

Edward Nelson that provides an axiomatic basis for a portion of the nonstandard analysis introduced by Abraham Robinson. Instead of adding new elements to...

In nonstandard analysis, a branch of mathematics, a hyperfinite set or *-finite set is a type of internal set. An internal set H of internal cardinality...

noted for his work in constructive mathematics. Bishop's review was harshly critical; see Criticism of nonstandard analysis. Shortly after, Martin Davis...