Potenzmenge

#Studium #Informatik #Definition #FoG #Mathematik #DS

Sei $A$ beliebige Menge. Dann heißt $P (A) ≜ {B ∣ B \subseteq A}$ #FoG
alternative Notation: $2^{A} ≜ P (A)$ #FoG
$P (M) := {U : U \subseteq M}$ #DS
alternative Notation: $P (M) := 2^{M}$ #DS

Proposition:

# (P (A)) = {\begin{cases} 2^{# (A)} & falls # (A) < \infty \\ \infty & falls # (A) = \infty \end{cases}

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