# Cardinality of a set

• Sep 23rd 2012, 06:15 AM
peyton1983
Cardinality of a set
What is the cardinality of the power set {NULL, a, {NULL}, {{NULL}}}? Why? I believe it is 3.
• Sep 23rd 2012, 08:47 AM
Plato
Re: Cardinality of a set
Quote:

Originally Posted by peyton1983
What is the cardinality of the power set {NULL, a, {NULL}, {{NULL}}}? Why? I believe it is 3.

To be very clear, the given set is $\displaystyle \left\{ {\emptyset ,\;a,\;\{ \emptyset \} ,\;\{ \{ \emptyset \} \} } \right\}$.

If that is correct, then that set contains four elements. So what is the carnality of its power set?
• Sep 25th 2012, 06:16 AM
emakarov
Re: Cardinality of a set
Quote:

Originally Posted by Plato
To be very clear, the given set is $\displaystyle \left\{ {\emptyset ,\;a,\;\{ \emptyset \} ,\;\{ \{ \emptyset \} \} } \right\}$.

If that is correct, then that set contains four elements.

Unless $\displaystyle a\in\left\{ {\emptyset ,\;\{ \emptyset \} ,\;\{ \{ \emptyset \} \} } \right\}$, in which case it contains three elements.