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Vollständige Induktion by Kock, Franziska

Vollständige Induktion

by Franziska Kock
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Book cover type: Paperback
  • ISBN13: 9783656360889
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 20
  • Original Price: USD 19.9
  • Language: German
  • Edition: N/A
  • Item Weight: 41 grams
  • BISAC Subject(s): Algebra / General

Facharbeit (Schule) aus dem Jahr 2012 im Fachbereich Lernmaterialien - Mathematik, Note: 1, Sprache: Deutsch, Abstract: In der Mathematik stö t man oft auf Zusammenhänge, die zunächst allgemein gültig erscheinen. So begegnet man in der Oberstufe zum Beispiel der Summenformel für die Zahlen 1 bis n. Diese ist beispielsweise für die Berechnung von Ober- und Untersummen unerlässlich. Doch um mit einer solchen Gleichung arbeiten zu können, muss man diese im Vorhinein allgemeingültig beweisen. Dazu kann man das Verfahren der vollständigen Induktion anwenden. Dieses ist eine der grundlegenden Beweismethoden in der Mathematik, mit welcher sich allgemeingültige Aussagen für natürliche Zahlen beweisen lassen. Seiner Wortherkunft nach (lat. "inductio") bedeutet das Wort Induktion "das Hineinführen" und die Methode der vollständigen Induktion wird oft als Schlussfolgerung "vom Besonderen auf das Allgemeine" definiert. Das Gegenteil hiervon ist die Deduktion, bei der vom "Allgemeinen auf das Einzelne" geschlossen wird. Ein einfaches, erklärendes Beispiel für eine Deduktion wäre zum Beispiel: "Alle Menschen haben einen Kopf. Peter ist ein Mensch. Folgerung: Peter hat einen Kopf" Anwendungsgebiete für dieses Beweisverfahren finden sich in allen Gebieten der Mathematik wie zum Beispiel der Geometrie, der Mengenlehre oder der Zahlentheorie.

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