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- Specker_sequence abstract "In computability theory, a Specker sequence is a computable, monotonically increasing, bounded sequence of rational numbers whose supremum is not a computable real number. The first example of such a sequence was constructed by Ernst Specker in 1949. The existence of Specker sequences has consequences for computable analysis. The fact that such sequences exist means that the collection of all computable real numbers does not satisfy the least upper bound principle of real analysis, even when considering only computable sequences. A common way to resolve this difficulty is to consider only sequences that are accompanied by a modulus of convergence; no Specker sequence has a computable modulus of convergence. The least upper bound principle has also been analyzed in the program of reverse mathematics, where the exact strength of this principle has been determined. In the terminology of that program, the least upper bound principle is equivalent to ACA0 over RCA0.".
- Specker_sequence thumbnail SuiteSpecker.svg?width=300.
- Specker_sequence wikiPageID "21535918".
- Specker_sequence wikiPageRevisionID "583489281".
- Specker_sequence hasPhotoCollection Specker_sequence.
- Specker_sequence subject Category:Computable_analysis.
- Specker_sequence comment "In computability theory, a Specker sequence is a computable, monotonically increasing, bounded sequence of rational numbers whose supremum is not a computable real number. The first example of such a sequence was constructed by Ernst Specker in 1949. The existence of Specker sequences has consequences for computable analysis.".
- Specker_sequence label "Specker sequence".
- Specker_sequence label "Specker-Folge".
- Specker_sequence label "Suite de Specker".
- Specker_sequence sameAs Specker-Folge.
- Specker_sequence sameAs Suite_de_Specker.
- Specker_sequence sameAs m.05h2rd6.
- Specker_sequence sameAs Q2308311.
- Specker_sequence sameAs Q2308311.
- Specker_sequence wasDerivedFrom Specker_sequence?oldid=583489281.
- Specker_sequence depiction SuiteSpecker.svg.
- Specker_sequence isPrimaryTopicOf Specker_sequence.
