Mathematik 1 at Hochschule Furtwangen

Flashcards and summaries for Mathematik 1 at the Hochschule Furtwangen

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Study with flashcards and summaries for the course Mathematik 1 at the Hochschule Furtwangen

Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

Rationale Zahlen ℚ

Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

Kommutativgesetz

Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

Die Mengen A und B heißen disjunkt (elementfremd)

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Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:


kartesische Produkt zweier Mengen A und B

Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

A ⊂ B

Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

Schnittmenge A∩B

Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

A ⊆ B

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Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

Assoziativgesetz

Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

Transitivität

Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

Symmetrischer Einschluss

Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

Symmetrische Differenz von Mengen

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Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

Komplementärmenge

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Exemplary flashcards for Mathematik 1 at the Hochschule Furtwangen on StudySmarter:

Mathematik 1

Rationale Zahlen ℚ

{x | x = a/b , a ∈ Z, b ∈ N+}

Mathematik 1

Kommutativgesetz

a + b = b + a und a · b = b · a

Mathematik 1

Die Mengen A und B heißen disjunkt (elementfremd)

wenn gilt A ∩ B = ∅

Mathematik 1


kartesische Produkt zweier Mengen A und B

ist die Menge
A×B := {(a, b) | a ∈ A und b ∈ B}

Mathematik 1

A ⊂ B

wenn jedes Element von A auch zu Menge B gehört

Mathematik 1

Schnittmenge A∩B

Menge aller Elemente, die sowohl zu A als auch zu B gehören:
... = {x | x ∈ A und x ∈ B}



Mathematik 1

A ⊆ B

wenn jedes
Element von A auch zur Menge B gehört (Teilmenge)

Mathematik 1

Assoziativgesetz

a + (b + c) = (a + b) + c und

 a · (b · c) = (a · b) · c

Mathematik 1

Transitivität

A ⊆ B und B ⊆ C → A ⊆ C

Mathematik 1

Symmetrischer Einschluss

A ⊆ B und B ⊆ A → A = B

Mathematik 1

Symmetrische Differenz von Mengen

Menge aller der Elemente,

die entweder nur in A oder nur in B enthalten sind:

A ∆  B := (A\B) ∪ (B\A)

Mathematik 1

Komplementärmenge

bzgl. einer Universalmenge M ist die
Menge:
A := M\A.
Die Komplementärmenge ist nur dann sinnvoll erklärt, wenn die Grundmenge M eindeutig gegeben ist

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