# ordered tuplet

The concept^{} of ordered $n$-tuplet is the generalization^{} of ordered pair^{} to $n$ items. For small values of $n$, the following are used:

$$\begin{array}{ccc}\hfill n\hfill & \hfill \text{\pi \x9d\x91\x9b\pi \x9d\x91\x8e\pi \x9d\x91\x9a\pi \x9d\x91\x92}\hfill & \hfill \text{\pi \x9d\x91\x92\pi \x9d\x91\u20af\pi \x9d\x91\x8e\pi \x9d\x91\x9a\pi \x9d\x91\x9d\pi \x9d\x91\x99\pi \x9d\x91\x92}\hfill \\ \hfill 3\hfill & \hfill \text{triplet}\hfill & \hfill (a,b,c)\hfill \\ \hfill 4\hfill & \hfill \text{quadruplet}\hfill & \hfill (a,b,c,d)\hfill \\ \hfill 5\hfill & \hfill \text{quintuplet}\hfill & \hfill (a,b,c,d,e)\hfill \\ \hfill 6\hfill & \hfill \text{sextuplet}\hfill & \hfill (a,b,c,d,e,f)\hfill \\ \hfill 7\hfill & \hfill \text{septuplet}\hfill & \hfill (a,b,c,d,e,f,g)\hfill \\ \hfill 8\hfill & \hfill \text{octuplet}\hfill & \hfill (a,b,c,d,e,f,g,h)\hfill \\ \hfill 9\hfill & \hfill \text{nonuplet}\hfill & \hfill (a,b,c,d,e,f,g,h,i)\hfill \\ \hfill 10\hfill & \hfill \text{decuplet}\hfill & \hfill (a,b,c,d,e,f,g,h,i,j)\hfill \end{array}$$ |

This notion can be defined set-theoretically in a number of ways. For convenience, we shall express two of these definitions for quintuplets β it is perfectly easy to generalize them to any other value of $n$.

One possibility is to build $n$-tuplets out of nested ordered pairs. In the case of our example $(a,b,c,d,e)$, the as a nested ordered pair looks like

$$(a,(b,(c,(d,e)))).$$ |

This form of is used in the programming language LISP.

Another possibility is to define $n$-tuplets as maps. In this way of thinking, a quintuplet is a function whose domain is the set $\{1,2,3,4,5\}$. In the case of our example, the function $f$ in question is defined as

$$\begin{array}{ccc}\hfill f\beta \x81\u2019(1)\hfill & \hfill =\hfill & \hfill a\hfill \\ \hfill f\beta \x81\u2019(2)\hfill & \hfill =\hfill & \hfill b\hfill \\ \hfill f\beta \x81\u2019(3)\hfill & \hfill =\hfill & \hfill c\hfill \\ \hfill f\beta \x81\u2019(4)\hfill & \hfill =\hfill & \hfill d\hfill \\ \hfill f\beta \x81\u2019(5)\hfill & \hfill =\hfill & \hfill e\hfill \end{array}$$ |

Especially with the second interpretation^{}, one sees that a synonym for βordered tupletβ is βfinite sequenceβ or βlistβ. For instance, a quintuplet can also be regarded as a sequence of five items or a list of five items.

Title | ordered tuplet |
---|---|

Canonical name | OrderedTuplet |

Date of creation | 2013-03-22 14:55:44 |

Last modified on | 2013-03-22 14:55:44 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 16 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 03-00 |

Synonym | tuplet |

Synonym | $n$-tuplet |

Synonym | $n$-tuplets |

Synonym | ordered $n$-tuplet |

Synonym | -tuplet |

Synonym | -tuplets |

Synonym | tuple |

Synonym | $n$-tuple |

Synonym | ordered $n$-tupule |

Synonym | -tuple |

Synonym | finite sequence |

Related topic | OrderedPair |

Related topic | GeneralizedCartesianProduct |

Defines | triplet |

Defines | quadruplet |

Defines | quintuplet |

Defines | sextuplet |

Defines | septuplet |

Defines | octuplet |

Defines | nonuplet |

Defines | decuplet |