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.

$\blacksquare$

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Sets and Logic: Exercise $4$