numbers - Is “-th” still a productive suffix in English?


The main question here is whether using -(e)th to create ordinals out of cardinals1 is still considered a productive suffix in English. Is it?


If so, then does it matter whether we are in a formal or informal register? Is it accepted in some contexts but not in others? Is it blocked by certain circumstances?


Consider these sorts of formations, arranged by least to most shocking; are they legal, illegal, or suspect?



  • the nth or nth item

  • the zeroth element

  • googolth for which item is number googol

  • epsilonth and ¹⁄epsilonᵗʰ (¹⁄epsilonth)

  • alphath or perhaps alphath

  • calculating the (1−alpha)th percentile

  • three-halfth for ³⁄₂ᵗʰ (³⁄₂th)

  • two-thirdth for ²⁄₃ᵗʰ (²⁄₃th



Footnotes:



  1. Such as we do with four > fourth, fifty > fiftieth, and billion > billionth



Answer



The short answer: yes, it is productive, because you can create words using this suffix that have never been heard before, such as the two-trillion-and-sixteenth coin in Scrooge McDuck's Money Bin. From Wikipedia:



A productive grammatical process defines an open class, one which admits new words or forms. Non-productive grammatical processes may be seen as operative within closed classes, but only previously formed and learned structures show the results of those processes. (Italics mine.)



The point of productivity is not that you can add a suffix to any word you please, but that it can be added to some words to create new words. Only if it cannot be added to any words in order to create new words is it said to be unproductive.


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