Cardinality/Examples/0 less than x less than 6

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

The cardinality of $S_2$ is given by:
 * $\card {S_2} = 5$

Proof
The elements of $S_2$, by definition, are those integers greater than $0$ and less than $6$.

That is:
 * $S_2 = \set {1, 2, 3, 4, 5}$

Thus $S_2$ has $5$ elements: $1, 2, 3, 4, 5$.

Hence the result by definition of cardinality.