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- Indecomposability abstract "In constructive mathematics, indecomposability or indivisibility (German: Unzerlegbarkeit, from the adjective unzerlegbar) is the principle that the continuum cannot be partitioned into two nonempty pieces. This principle was established by Brouwer in 1928 using intuitionistic principles, and can also be proven using Church's thesis. The analogous property in classical analysis is the fact that any continuous function from the continuum to {0,1} is constant.It follows from the indecomposability principle that any property of real numbers that is decided (each real number either has or does not have that property) is in fact trivial (either all the real numbers have that property, or else none of them do). Conversely, if a property of real numbers is not trivial, then the property is not decided for all real numbers. This contradicts the law of the excluded middle, according to which every property of the real numbers is decided; so, since there are many nontrivial properties, there are many nontrivial partitions of the continuum.In CZF, it is consistent to assume the universe of all sets is indecomposable—so that any class for which membership is decided (every set is either a member of the class, or else not a member of the class) is either empty or the entire universe.".
- Indecomposability wikiPageExternalLink Unzerlegbarkeit:JSL%20copy.pdf.
- Indecomposability wikiPageExternalLink tklracend.pdf.
- Indecomposability wikiPageID "17422461".
- Indecomposability wikiPageLength "2667".
- Indecomposability wikiPageOutDegree "14".
- Indecomposability wikiPageRevisionID "632854039".
- Indecomposability wikiPageWikiLink Category:Constructivism_(mathematics).
- Indecomposability wikiPageWikiLink Churchs_thesis_(constructive_mathematics).
- Indecomposability wikiPageWikiLink Constructive_analysis.
- Indecomposability wikiPageWikiLink Constructive_mathematics.
- Indecomposability wikiPageWikiLink Constructive_set_theory.
- Indecomposability wikiPageWikiLink Constructivism_(mathematics).
- Indecomposability wikiPageWikiLink Constructivist_analysis.
- Indecomposability wikiPageWikiLink Continuum_(set_theory).
- Indecomposability wikiPageWikiLink Indecomposable_continuum.
- Indecomposability wikiPageWikiLink Journal_of_Symbolic_Logic.
- Indecomposability wikiPageWikiLink L._E._J._Brouwer.
- Indecomposability wikiPageWikiLink Law_of_excluded_middle.
- Indecomposability wikiPageWikiLink Law_of_the_excluded_middle.
- Indecomposability wikiPageWikiLink Luitzen_Egbertus_Jan_Brouwer.
- Indecomposability wikiPageWikiLink Mathematical_analysis.
- Indecomposability wikiPageWikiLink Partition_of_a_set.
- Indecomposability wikiPageWikiLink Springer_Science+Business_Media.
- Indecomposability wikiPageWikiLink The_Journal_of_Symbolic_Logic.
- Indecomposability wikiPageWikiLink Trivial_(mathematics).
- Indecomposability wikiPageWikiLink Triviality_(mathematics).
- Indecomposability wikiPageWikiLinkText "Indecomposability".
- Indecomposability wikiPageWikiLinkText "indecomposability".
- Indecomposability hasPhotoCollection Indecomposability.
- Indecomposability wikiPageUsesTemplate Template:Cite_book.
- Indecomposability wikiPageUsesTemplate Template:Cite_journal.
- Indecomposability wikiPageUsesTemplate Template:Lang-de.
- Indecomposability wikiPageUsesTemplate Template:Other_uses.
- Indecomposability subject Category:Constructivism_(mathematics).
- Indecomposability hypernym Principle.
- Indecomposability type Airline.
- Indecomposability type Article.
- Indecomposability type Article.
- Indecomposability type Theory.
- Indecomposability comment "In constructive mathematics, indecomposability or indivisibility (German: Unzerlegbarkeit, from the adjective unzerlegbar) is the principle that the continuum cannot be partitioned into two nonempty pieces. This principle was established by Brouwer in 1928 using intuitionistic principles, and can also be proven using Church's thesis.".
- Indecomposability label "Indecomposability".
- Indecomposability sameAs Unzerlegbarkeit.
- Indecomposability sameAs m.04659kd.
- Indecomposability sameAs Q3552056.
- Indecomposability sameAs Q3552056.
- Indecomposability wasDerivedFrom Indecomposability?oldid=632854039.
- Indecomposability isPrimaryTopicOf Indecomposability.