Cardinality/Examples/x^2-x

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

where $S_1 = \set {-1, 0, 1}$.

The cardinality of $S_3$ is given by:
 * $\card {S_3} = 2$

Proof
The elements of $S_3$ can be found by calculation:

Thus by definition of set:
 * $S_3 = \set {0, 2}$

Thus $S_3$ has $2$ elements: $0, 2$.

Hence the result by definition of cardinality.