Mapping/Football game/Goal scorer/Example

We consider a football game as the mapping which assigns, to every goal of team ${}A$, the corresponding goal scorer. Suppose that there are no own goals and no changes. The goals of ${}A$ are numbered by ${}1,2,\ldots ,n$. Then we have a mapping

$\psi \colon \{1,\ldots ,n\}\longrightarrow A=\{{\text{player }}1,\,{\text{player }}2,\ldots ,{\text{player }}11\},$

given by

${}\psi (i)={\text{ the player who has scored the }}i{\text{-th goal}}\,.$

The injectivity of ${}\psi$ means that every player has scored at most one goal, the surjectivity means that every player has scored at least one goal.