Math 2.0

Mathematical logic and foundations Constructive mathematics Concept

Constructive analysis

Builds on ConstructivismReal numbersCauchy sequenceIntermediate value theorem

Summary

Constructive analysis is mathematical analysis carried out under the principles of constructivism. Real numbers are given by Cauchy sequences of rationals with an explicit rate of convergence, and every existence proof must give an approximation method. Bishop's book "Foundations of Constructive Analysis" of 1967 showed that a large part of classical analysis can be developed in this way. Its theorems are also valid classically, and they carry algorithms.

Reading path

To understand this page from the ground up, read these 27 pages in order. The foundations come first.

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Cauchy sequence, concept, no evidence levelCauchy sequenceconceptLimit point of a set, definition, no evidence levelLimit point of a setdefinitionProposition, concept, no evidence levelPropositionconceptReal numbers, object, no evidence levelReal numbersobjectLimit of a function, definition, no evidence levelLimit of a functiondefinitionConjunction, definition, no evidence levelConjunctiondefinitionDisjunction, definition, no evidence levelDisjunctiondefinitionImplication, definition, no evidence levelImplicationdefinitionNegation, definition, no evidence levelNegationdefinitionPredicate, definition, no evidence levelPredicatedefinitionContinuity at a point, definition, no evidence levelContinuity at a pointdefinitionBiconditional, definition, no evidence levelBiconditionaldefinitionTruth table, concept, no evidence levelTruth tableconceptLaw of excluded middle, statement, no evidence levelLaw of excluded middlestatementModus ponens, concept, no evidence levelModus ponensconceptExistential quantifier, definition, no evidence levelExistential quantifierdefinitionContinuous function, definition, no evidence levelContinuous functiondefinitionPropositional logic, concept, no evidence levelPropositional logicconceptMathematical proof, concept, no evidence levelMathematical proofconceptIntermediate value theorem, statement, no evidence levelIntermediate value th…statementTautology, definition, no evidence levelTautologydefinitionConstructive proof, concept, no evidence levelConstructive proofconceptLogical equivalence, definition, no evidence levelLogical equivalencedefinitionDouble negation law, statement, no evidence levelDouble negation lawstatementProof by contradiction, concept, no evidence levelProof by contradictionconceptConstructivism, concept, no evidence levelConstructivismconceptConstructive analysis, concept, no evidence levelConstructive analysisconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Cauchy sequence concept
  2. Limit point of a set definition
  3. Proposition concept
  4. Real numbers object
  5. Limit of a function definition
  6. Conjunction definition
  7. Disjunction definition
  8. Implication definition
  9. Negation definition
  10. Predicate definition
  11. Continuity at a point definition
  12. Biconditional definition
  13. Truth table concept
  14. Law of excluded middle statement
  15. Modus ponens concept
  16. Existential quantifier definition
  17. Continuous function definition
  18. Propositional logic concept
  19. Mathematical proof concept
  20. Intermediate value theorem statement
  21. Tautology definition
  22. Constructive proof concept
  23. Logical equivalence definition
  24. Double negation law statement
  25. Proof by contradiction concept
  26. Constructivism concept
  27. Constructive analysis concept

Further reading

  1. Web https://en.wikipedia.org/wiki/Constructive_analysis
About this page
TagHEB1VQW0DQ
URIm2://HEB1VQW0DQ
Kindconcept
WritingW0 stub
MSC03F60, 03F65
UsesConstructivism, Real numbers, Cauchy sequence, Intermediate value theorem
Same as
Changed2 November 2026

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