Übersetzung und Analyse von Wörtern durch künstliche Intelligenz ChatGPT
Auf dieser Seite erhalten Sie eine detaillierte Analyse eines Wortes oder einer Phrase mithilfe der besten heute verfügbaren Technologie der künstlichen Intelligenz:
- wie das Wort verwendet wird
- Häufigkeit der Nutzung
- es wird häufiger in mündlicher oder schriftlicher Rede verwendet
- Wortübersetzungsoptionen
- Anwendungsbeispiele (mehrere Phrasen mit Übersetzung)
- Etymologie
overspill - Übersetzung nach arabisch
overspill
Definition
Wikipedia
In nonstandard analysis, a branch of mathematics, overspill (referred to as overflow by Goldblatt (1998, p. 129)) is a widely used proof technique. It is based on the fact that the set of standard natural numbers N is not an internal subset of the internal set *N of hypernatural numbers.
By applying the induction principle for the standard integers N and the transfer principle we get the principle of internal induction:
For any internal subset A of *N, if
- 1 is an element of A, and
- for every element n of A, n + 1 also belongs to A,
then
- A = *N
If N were an internal set, then instantiating the internal induction principle with N, it would follow N = *N which is known not to be the case.
The overspill principle has a number of useful consequences:
- The set of standard hyperreals is not internal.
- The set of bounded hyperreals is not internal.
- The set of infinitesimal hyperreals is not internal.
In particular:
- If an internal set contains all infinitesimal non-negative hyperreals, it contains a positive non-infinitesimal (or appreciable) hyperreal.
- If an internal set contains N it contains an unlimited (infinite) element of *N.
