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 less 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 $$x^2 + xy + y^2$$, is called a “binary quadratic”: due to two variables,  due to degree two. See English polynomial degrees for a full list.