# Appendix:English arities and adicities

English has two series of arities, functioning as distributive numbers: one from Latin (arities), one from Ancient Greek (adicities). The Latinate series is commonly used, particularly *binary,* while the Ancient Greek one is much more common.

The Latinate series is frequently confused with ordinal numbers, as both end in *-ary*. This is most significant for *quaternary* (arity, used for both) vs. *quartary* (ordinal) and *novenary* (arity) vs. *nonary* (ordinal, used for both). The Latinate series is also used for names of the lower positional numeral systems (binary, ternary), but not from base-8 (octal, not *octonary) upwards.

For polynomials, both these numbering systems are used at once. For example, a degree two polynomial in two variables, such as , is called a “binary quadratic”: *binary* due to two variables, *quadratic* due to degree two. See English polynomial degrees for a full list.

number | Latinate | Grecian |
---|---|---|

0 | nullary | niladic, medadic |

1 | unary | monadic |

2 | binary | dyadic |

3 | ternary | triadic |

4 | quaternary | tetradic |

5 | quinary | pentadic |

6 | senary | hexadic |

7 | septenary | heptadic |

8 | octonary | ogdoadic |

9 | novenary | enneadic |

10 | denary | decadic |

11 | undenary | endecadic |

12 | duodenary | dodecadic |

20 | vigenary | icosadic |