Insimul potentia

In mathematica, le insimul potentia es le insimul de omne subinsimules de un certe insimul. Le insimul de potentia de $A$ es habitualmente notate como ${\mathfrak {P}}(A)$, ${\mathcal {P}}(A)$, $\wp (A)$, o $2^{A}$. In vice de insimul potentia, on alsi pote dicer insimul del subinsimules. Le numero cardinal del insimul potentia del insimul $A$ es $2$ elevate al numero cardinal de $A$: $|{\mathcal {P}}(A)|=2^{|A|}$ o, in altere maniera de scriber, ${\big |}2^{A}{\big |}=2^{|A|}$.

Exemplos

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

Vide etiam

• Producto cartesian