what is the cardinality of this sets:

$\displaystyle a.) \left\{{\varnothing}, \left\{{\varnothing}\right\}, \left\{{\varnothing}, \left\{{\varnothing}\right\}\right\}\right\}$

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- Jun 25th 2007, 03:06 PMTheRekzempty set question
what is the cardinality of this sets:

$\displaystyle a.) \left\{{\varnothing}, \left\{{\varnothing}\right\}, \left\{{\varnothing}, \left\{{\varnothing}\right\}\right\}\right\}$ - Jun 25th 2007, 03:24 PMThePerfectHacker
- Jun 25th 2007, 03:33 PMPlato
First, I must say that I do not think that you are asking the question that you mean to ask.

Because, I see only one element of the set of triples, 3-tuples.

Now, I am of course aware that a set of ordered pairs is defined as sets of sets: the pair $\displaystyle

\left( {a,b} \right) = \left\{ {\left\{ a \right\},\left\{ {a,b} \right\}} \right\}$

And we define the triple $\displaystyle \left( {a,b,c} \right) = \left( {\left( {a,b} \right),c} \right)$.

Therefore, have you asked the question you meant to ask? - Jun 25th 2007, 04:41 PMTheRekz
- Jun 26th 2007, 03:48 AMPlato
Because you edited the question to change ( to {, the answer is 3.