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Forum Studenti •esercizio hard
Pagina 1 di 1

esercizio hard

Inviato: martedì 30 settembre 2008, 23:20
da Roberto_dirienzo
qual'è la soluzione dell'esercizio hard che il professore ha dato alla fine della seconda ora ...

| p(p(p(insieme vuoto)))|

io ho ragionato cosi:

l'insieme vuoto è sottoinsieme ti qualunque insieme quindi anche dell'insieme vuoto stesso

Per sua natura l'insieme vuoto non possiede nessun altro sottoinsieme.

Di conseguenza L'insieme delle parti dell'insieme vuoto è costituito dal solo insieme vuoto.

reiterando per 3 volte quanto detto è facile concludere che la cardinalità è 1.

Inviato: mercoledì 15 ottobre 2008, 0:16
da Distruggiu

Inviato: mercoledì 15 ottobre 2008, 21:49
da Lethal Dosage_88

Inviato: giovedì 16 ottobre 2008, 20:14
da Tavaguet

Inviato: sabato 20 dicembre 2008, 18:26
da Ispa
io invece ho ragionato cosi' :

0 = Insieme vuoto
P = Insieme delle parti
_________________________


0={}
insieme avente nessun elemento (zero elementi)
per tanto |P(0)| = 2^0 = 1 elemento

P(0)={ 0 }
insieme avente 1 solo elemento ( l'insieme vuoto)
per tanto |P (P(0))| = 2^1 = 2 elementi


P (P(0)) = { 0, {0}}
insieme avente 2 elementi (l'insieme vuoto e l'insieme che contiene l'elemento insieme vuoto)
per tanto|P (P(P(0)))|= 2^2 = 4 elementi

P (P(P(0))) = { 0, {0}, {{0}}, {0,{0}} }

insieme avente 4 elementi ( insieme vuoto, l'insieme contentenete l'elemento insieme vuoto, l'insieme contentente l'elemento "insieme che contenente l'insieme vuoto", l'insieme delle parti dell'insieme P (P(0)) che sarebbe il precedente )

perdonatementi il ragionamento contorto......

quindi 4 elementi totali che ne pensate?


inoltre cosi' credo anche di aver dimostratrato la regola di cardinalità :
|A| = K => |A(P)| = 2^K

no?



Inviato: domenica 8 novembre 2009, 12:49
da fabry9002

Inviato: mercoledì 11 novembre 2009, 19:33
da g.masullo
Molto brutalmente, la concezione dell'insieme vuoto è assimilabile a quella di un astuccio vuoto

E' vuoto, ma c'è. Se quindi considero la cardinalità di 4 astucci uno dentro l altro, sarà banalmente 4.

:D