Which ordinal indicator, if any, should be used on symbolic math variables?

Question

Consider:

• “the n-th root of x”
• “the a-th derivative of b”

and even more troublesome:

• “the ϑ-th something…” (thetath?)

Is there a rule for which ordinal indicator to use on a name, or symbolic variable?

I have seen “n-th” used in various places, but I cannot say the same for other variable names (x, y, ϑ…)

Is “-th” the preferred indicator for unknown quantities? Is it even acceptable to use one, or should the sentence be rephrased into “the something of order ϑ” whenever possible?

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NB. This question was never about the typesetting choice of “n-th” vs. “nth,” or even n^th, but about the use of an ordinal indicator on symbolic variables: short names that are used to represent unknown quantities.

Answer 1

In non-mathematical contexts, such as colloquial use of "the nth degree", "the n^th degree", or "the n-th degree" then all have a justification in analogy to other forms, and either could be used. I'd recommend using the closed form nth only with n because it's more common than other possibilities, which reduces the possibility of confusion. Indeed dictionaries often list nth as a word.

In mathematical contexts there's a possibility of confusion with the superscript form on that it could be read as "to the power of th", that would lead me to favour the hyphenated form.

Answer 2

It all depends on the last digit of the last number. if it is 1 we use -st. 2 uses -nd. 3 uses -rd. Everything else uses -th, so the general case is likely to be -th and is named that way.

Answer 3

Style guides undoubtedly differ on this point. The only specific guidance I've been able to find in the style guides I consulted, however, is from The Chicago Manual of Style, sixteenth edition (2010):

9.6 Ordinals. ... In the expression "nth degree," Chicago style is to italicize the n (see also 7.59).

At 7.59, Chicago lays out its general preference for italicizing standalone letters when they are serving the role of letters rather than words:

7.59 Letters as letters. Individual letters and combinations of letters of the Latin alphabet are usually italicized. [Examples:]

the letter q

a lowercase n

a capital W

The plural is usually formed by adding s or es.

He signed the document with an X.

I need a word with two e's and three s's.

The upshot of guideline 7.59 is that Chicago advocates treating single letter variables (such as n) as "letters as letters," and hence italicizes them. The upshot of guideline 9.6 is that Chicago advocates treating the ordinal form of a letter variable as the (italic) letter with the ordinal suffix (usually th) closed up. Hence the preference for nth—and presumably, by like reasoning, for (n + 1)th.