𝔖 Bobbio Scriptorium
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Completeness for systems including real numbers

✍ Scribed by W. Balzer; M. Reiter

Publisher
Springer Netherlands
Year
1989
Tongue
English
Weight
613 KB
Volume
48
Category
Article
ISSN
0039-3215

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πŸ“œ SIMILAR VOLUMES

Real numbers and other completions
Real numbers and other completions
✍ Fred Richman πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 135 KB

## Abstract A notion of completeness and completion suitable for use in the absence of countable choice is developed. This encompasses the construction of the real numbers as well as the completion of an arbitrary metric space. The real numbers are characterized as a complete Archimedean Heyting fi

Completeness of Orthonormal Wavelet Syst
Completeness of Orthonormal Wavelet Systems for Arbitrary Real Dilations
✍ Richard S. Laugesen πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 174 KB

It is shown that the discrete Calderón condition characterizes completeness of orthonormal wavelet systems, for arbitrary real dilations. That is, if a > 1, b > 0, and the system = {a j/2 ψ(a j xbk) A new proof of the Second Oversampling Theorem is found, by similar methods.

Revisiting the hybrid real number system
Revisiting the hybrid real number system
✍ E. Escultura; T. Gnana Bhaskar; V. Lakshmikantham; S. Leela πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier 🌐 English βš– 420 KB

The hybrid real number system consisting of terminating and nonterminating decimals, dark numbers, dual dark numbers, involving the notions of personal infinities and the impersonal infinity has been discussed. Some algebraic properties of dark numbers and dual dark numbers are discussed.