Diskrete Mathematik at Hochschule Bonn-Rhein-Sieg

Flashcards and summaries for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg

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Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Def. Schnittmenge

Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Def. Komplement

Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Thm. Transitivität von ⊆

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Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Definition einer Menge    

Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Definition: Leere Menge    

Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Gleichheit von Zahlen

Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Thm. Isotonie1 von ℘

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Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Def. Potenzmenge

Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Def =<

Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Thm. Kardinalität der Potenzmenge

Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Definition Inkrement (y = x +1)
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Thm. Kardinalität

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Exemplary flashcards for Diskrete Mathematik at the Hochschule Bonn-Rhein-Sieg on StudySmarter:

Diskrete Mathematik

Def. Schnittmenge

u ∩ v := {x | x ∈ u und x ∈ v} = u ∪ v

Diskrete Mathematik

Def. Komplement

u := {x | x /∈ u}

Diskrete Mathematik

Thm. Transitivität von ⊆

u ⊆ v und v ⊆ w dann gilt u ⊆ w.

Diskrete Mathematik

Definition einer Menge    
Eine Menge ist eine Zusammenfassung wohl unterscheidbarer Objekte aus einem Universum.

Diskrete Mathematik

Definition: Leere Menge    
Die leere Menge ist definiert als die Menge, die keine Elemente enthält.

Diskrete Mathematik

Gleichheit von Zahlen
Zwei Zahlen sind gleich, wenn sie die Kardinalität der gleichen Ordinalzahl beschreiben.

Diskrete Mathematik

Thm. Isotonie1 von ℘

u ⊆ v =⇒ ℘(u) ⊆ ℘(v).

Diskrete Mathematik

Def. Potenzmenge

Die Potenzmenge ℘(u) einer Menge u ist die Menge aller Teilmengen von u: ℘(u) := {v | v ⊆ u}

Diskrete Mathematik

Def =<
n ist kleiner oder gleich m wenn
n Teilmenge von m

Diskrete Mathematik

Thm. Kardinalität der Potenzmenge

C(℘(u)) = 2^C(u).

Diskrete Mathematik

Definition Inkrement (y = x +1)
Wir schreiben y = x + 1 wenn, y = x´, also wenn
y = x oder {x}

Diskrete Mathematik

Thm. Kardinalität

u ⊆ v dann gilt C(u) ≤ C(v).


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