The

**canonical projection**on $X$ with respect to $i \in J$ is the D18: Map \begin{equation} X \to X_i, \quad \{ x_j \}_{j \in J} \mapsto x_i \end{equation}

▼ | Set of symbols |

▼ | Alphabet |

▼ | Deduction system |

▼ | Theory |

▼ | Zermelo-Fraenkel set theory |

▼ | Set |

▼ | Binary cartesian set product |

▼ | Binary relation |

▼ | Map |

▼ | Cartesian product |

Definition D327

Canonical set projection

Formulation 0

Let $X = \prod_{j \in J} X_j$ be a D326: Cartesian product.

The**canonical projection** on $X$ with respect to $i \in J$ is the D18: Map
\begin{equation}
X \to X_i, \quad
\{ x_j \}_{j \in J} \mapsto x_i
\end{equation}

The

Results

▶ | Element in countable cartesian product iff components in images of canonical projections |

▶ | Element in finite cartesian product iff components in images of canonical projections |