Cardinality/Examples

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Examples of Cardinality

Let:

\(\displaystyle S_1\) \(=\) \(\displaystyle \set {-1, 0, 1}\)
\(\displaystyle S_2\) \(=\) \(\displaystyle \set {x \in \Z: 0 < x < 6}\)
\(\displaystyle S_3\) \(=\) \(\displaystyle \set {x^2 - x: x \in S_1}\)
\(\displaystyle S_4\) \(=\) \(\displaystyle \set {X \in \powerset {S_2}: \card X = 3}\)
\(\displaystyle S_5\) \(=\) \(\displaystyle \powerset \O\)


Cardinality of $S_1 = \set {-1, 0, 1}$

The cardinality of $S_1$ is given by:

$\card {S_1} = 3$


Cardinality of $S_2 = \set {x \in \Z: 0 < x < 6}$

The cardinality of $S_2$ is given by:

$\card {S_2} = 5$


Cardinality of $S_3 = \set {x^2 - x: x \in S_1}$

The cardinality of $S_3$ is given by:

$\card {S_3} = 2$


Cardinality of $S_4 = \set {X \in \powerset {S_2}: \card X = 3}$

The cardinality of $S_4$ is given by:

$\card {S_4} = 10$


Cardinality of $S_5 = \powerset \O$

The cardinality of $S_5$ is given by:

$\card {S_5} = 1$


Sources