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

Hilbert and Bernays, the constructive recursive mathematics of Shanin and Markov, and Bishop's program of constructive analysis. Constructivism also includes...

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

of constructive, rather than classical, logic and set theory. Intuitionistic analysis, which is developed from constructive logic like constructive analysis...

known for his work on analysis. He is best known for developing constructive analysis in his 1967 Foundations of Constructive Analysis, where he proved most...

not in intuitionistic constructive mathematics. However, many particular instances of it are nevertheless provable in a constructive context as well. The...

constructive mathematical theories tend to prove classically equivalent reformulations of classical theorems. For example, in constructive analysis,...

functional analysis that can be carried out in a computable manner. The field is closely related to constructive analysis and numerical analysis. A notable...

In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for...

definitions and theorems in constructive analysis. Regular Cauchy sequences were used by Bishop (2012) and by Bridges (1997) in constructive mathematics textbooks...

known for his work on analysis. He is best known for developing constructive analysis in his 1967 Foundations of Constructive Analysis, where he proved most...

of its definitions and methods are inspired by previous work in constructive analysis and proof theory. The use of second-order arithmetic also allows...

greatly increased by Errett Bishop's influential book Foundations of Constructive Analysis. A different objection put forth by Henri Poincaré is that defining...

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

important in numerical analysis and constructive mathematics, since many theorems that can be proved for nonseparable spaces have constructive proofs only for...

κ-saturated extension can be constructed. Calculus Made Easy Constructive nonstandard analysis Differential_(mathematics) Elementary Calculus: An Infinitesimal...

using proofs by contradiction. In weaker foundations such as in constructive analysis where the law of the excluded middle does not hold, the full form...

space. Constructive analysis mathematical analysis done according to the principles of constructive mathematics. This differs from classical analysis. Constructive...

Bridges, Constructive analysis, Springer-Verlag, 1985. Fred Richman, "Constructive mathematics without choice", in: Reuniting the Antipodes—Constructive and...

Robinson's infinitesimals in the classroom. In his Foundations of Constructive Analysis (1967, page ix), Bishop wrote: Our program is simple: To give numerical...

Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data...

approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles...

Indecomposability (intuitionistic logic), a principle in constructive analysis and in computable analysis Indecomposability of a polynomial in polynomial decomposition...

Steklova 38 (1951) 176-189) Kushner, Boris A. (1999-05-28). "Markov's constructive analysis; a participant's view". Theoretical Computer Science. 219 (1–2):...

open problems". Michel Waldschmidt. Mark Bridger (2007). Real Analysis: A Constructive Approach through Interval Arithmetic. John Wiley & Sons. ISBN 978-1-470-45144-8...

1007/s10701-017-0078-3. S2CID 118954904. Bishop, Errett; Bridges, Douglas (1985), Constructive analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles...

Bishop publishes Foundations of Constructive Analysis, proving theorems in real analysis using constructive analysis. Michael Goldberg demonstrates that...

theorem as an exercise (Problem 2 on page 58 in Foundations of constructive analysis). The theorem is a foregone conclusion over classical logic, where...

usual statement of the Sylvester–Gallai theorem is not valid in constructive analysis, as it implies the lesser limited principle of omniscience, a weakened...

the most important theorems in real analysis as constructive analysis in his 1967 Foundations of Constructive Analysis. Finitism is an extreme form of constructivism...