## Restricted image

### Set

context | $ f:X\to Y $ |

context | $ S\subseteq X $ |

postulate | $ f(S)\equiv \mathrm{im}(f|_S) $ |

### Discussion

The notation $f(S)$ is overloading $f$, as $S$ is not actually in the domain $X$ of $f$.

### Reference

Wikipedia: Image

context | $ f:X\to Y $ |

context | $ S\subseteq X $ |

postulate | $ f(S)\equiv \mathrm{im}(f|_S) $ |

The notation $f(S)$ is overloading $f$, as $S$ is not actually in the domain $X$ of $f$.

Wikipedia: Image