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Insimul potentia

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De Wikipedia, le encyclopedia libere

In mathematica, leinsimul potentia^[1] es leinsimul de omnesubinsimules de un certe insimul. Le insimul de potentia de $A {\displaystyle A}$ es habitualmente notate como ${\mathfrak {P}}(A)$ , ${\mathcal {P}}(A)$ , $\wp (A)$ , o $2^{A}$ . In vice deinsimul potentia, on alsi pote dicerinsimul del subinsimules. Lenumero cardinal del insimul potentia del insimul $A {\displaystyle A}$ es $2 {\displaystyle 2}$ elevate al numero cardinal de $A {\displaystyle A}$ : $|{\mathcal {P}}(A)|=2^{|A|}$ o, in altere maniera de scriber, ${\big |}2^{A}{\big |}=2^{|A|}$ .

Exemplos

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${\mathcal {P}}(\{1\})={\big \{}\emptyset ;\{1\}{\big \}}$ ;\{1\}{\big \}}} con $|{\mathcal {P}}(\{1\})|=2^{1}=2$ .
${\mathcal {P}}(\{1;2\})={\big \{}\emptyset ;\{1\};\{2\};\{1;2\}{\big \}}$ ;\{1\};\{2\};\{1;2\}{\big \}}} con $|{\mathcal {P}}(\{1;2\})|=2^{2}=4$ .
${\mathcal {P}}(\{1;2;3\})={\big \{}\emptyset ;\{1\};\{2\};\{3\};\{1;2\};\{1;3\};\{2;3\};\{1;2;3\}{\big \}}$ ;\{1\};\{2\};\{3\};\{1;2\};\{1;3\};\{2;3\};\{1;2;3\}{\big \}}} con $|{\mathcal {P}}(\{1;2;3\})|=2^{3}=8$ .
${\mathcal {P}}(\{1;2;3;4\})={\big \{}\emptyset ;\{1\};\{2\};\{3\};\{4\};\{1;2\};\{1;3\};\{1;4\},\{2;3\};\{2;4\};\{3;4\};\{1;2;3\};\{1;2;4\};\{1;3;4\};\{2;3;4\};\{1;2;3;4\}{\big \}}$ ;\{1\};\{2\};\{3\};\{4\};\{1;2\};\{1;3\};\{1;4\},\{2;3\};\{2;4\};\{3;4\};\{1;2;3\};\{1;2;4\};\{1;3;4\};\{2;3;4\};\{1;2;3;4\}{\big \}}} con $|{\mathcal {P}}(\{1;2;3;4\})|=2^{4}=16$ .

Vide etiam

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Referentias

↑Derivation (in ordine alphabetic):(ca) Conjunt de les parts ||(de) Potenzmenge ||(en) Power set ||(es) Conjunto potencia ||(fr) Ensemble des parties d'un ensemble ||(it) Insieme delle parti ||(pt) Conjunto de partes ||(ro) ||(ru) Множество всех подмножеств

Obtenite de “https://ia.wikipedia.org/w/index.php?title=Insimul_potentia&oldid=660566”

Theoria de insimules

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