# Mapping/Examples/Arbitrary Sets of Students

## Example of Mapping

Consider the indexed family as defined in Arbitrary Sets of Students:

Let $S$ be the set of students at a given university.

Let:

$A_1$ denote the set of first year students
$A_2$ denote the set of second year students
$A_3$ denote the set of third year students
$A_4$ denote the set of fourth year students.

We have:

$I = \set {1, 2, 3, 4}$ is an indexing set.

Hence $\alpha: I \to S$ is an indexing function on $S$.

Hence:

$\ds \bigcup_{\alpha \mathop \in I} A_\alpha =$ the set of all undergraduates at the university

and:

$\ds \bigcap_{\alpha \mathop \in I} A_\alpha = \O$

where $\ds \bigcup_{\alpha \mathop \in I} A_\alpha$ and $\ds \bigcap_{\alpha \mathop \in I} A_\alpha$ denote the union of $\family {A_\alpha}$ and intersection of $\family {A_\alpha}$ respectively.

The indexing function $\alpha: I \to S$ which establishes a correspondence between elements of $I$ and $S$ is an example of a mapping.