Cardinality of a set

**peyton1983** · September 23rd 2012, 06:15 AM

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

**Plato** · September 23rd 2012, 08:47 AM

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 $\left\{ {\emptyset ,\;a,\;\{ \emptyset \} ,\;\{ \{ \emptyset \} \} } \right\}$ .

If that is correct, then that set contains four elements. So what is the carnality of its power set?

**emakarov** · September 25th 2012, 06:16 AM

Originally Posted by Plato

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

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

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

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