Über die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen¶
Cantor, G. (1872). Über die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen. Stetigkeit und irrationale Zahlen, 123-132.
Cited by¶
1 citation across 1 artifact.
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Primes¶
- Completeness
- The Cauchy criterion of 1821 (Cauchy, Cours d'analyse) is the originating articulation of the no-gaps idea in analysis: a sequence converges if and only if it is Cauchy, which characterises completeness as the structural property of a metric system in which internal sequence-processes terminate inside the system. Completeness is the no-gaps-in-the-structure principle that names the condition under which a system's internal processes (convergence, deduction, coverage, the construction of canonical extensions) have their natural terminations inside the system itself rather than escaping to a larger ambient structure.
This sourceVieweg, Braunschweig (constructs the reals via Dedekind cuts). The two independent constructions establish the metric and order completeness of the reals as the canonical completion of the rationals.
- The Cauchy criterion of 1821 (Cauchy, Cours d'analyse) is the originating articulation of the no-gaps idea in analysis: a sequence converges if and only if it is Cauchy, which characterises completeness as the structural property of a metric system in which internal sequence-processes terminate inside the system. Completeness is the no-gaps-in-the-structure principle that names the condition under which a system's internal processes (convergence, deduction, coverage, the construction of canonical extensions) have their natural terminations inside the system itself rather than escaping to a larger ambient structure.
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Registry ID ref:a6554e194a17 · see in the full table