Specker Sequence
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High Quality Content by WIKIPEDIA articles! In computability theory, a Specker sequence is a computable, strictly 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. A common way to resolve this difficulty is to consider only sequences that…mehr

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High Quality Content by WIKIPEDIA articles! In computability theory, a Specker sequence is a computable, strictly 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. 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.