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- Bar_induction abstract "Bar induction is a reasoning principle used in intuitionistic mathematics, introduced by L.E.J. Brouwer.It is useful in giving constructive versions of classical results.It is based on an inductive argument.The goal of the principle is to prove properties of infinite streams of natural numbers, called choice sequences in intuitionistic terminology, by inductively reducing them to decidable properties of finite lists.Given two predicates R and S on finite lists of natural numbers, assume the following conditions hold: R is decidable; Every choice sequence has a finite prefix satisfying R (this is expressed by saying that R is a bar); Every list satisfying R also satisfies S; If all extensions of a list by one element satisfy S, then that list also satisfies S.Then we can conclude that S holds for the empty list.".
- Bar_induction wikiPageID "5492505".
- Bar_induction wikiPageRevisionID "500789902".
- Bar_induction first "A.G.".
- Bar_induction hasPhotoCollection Bar_induction.
- Bar_induction id "Bar_induction".
- Bar_induction last "Dragalin".
- Bar_induction oldid "12849".
- Bar_induction title "Bar induction".
- Bar_induction subject Category:Constructivism_(mathematics).
- Bar_induction subject Category:Mathematical_induction.
- Bar_induction comment "Bar induction is a reasoning principle used in intuitionistic mathematics, introduced by L.E.J.".
- Bar_induction label "Bar induction".
- Bar_induction sameAs m.0dp6rr.
- Bar_induction sameAs Q4857985.
- Bar_induction sameAs Q4857985.
- Bar_induction wasDerivedFrom Bar_induction?oldid=500789902.
- Bar_induction isPrimaryTopicOf Bar_induction.