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Suppose that I would like to say "Let f(x) be an N-times differentiable function."

Should it be "N-times" or "N times", and why?

null
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    Does this answer your question? Student t-distribution: why the dash { 'hyphens: numerals and single letters Hyphenate numerals or single letters and the words they modify: e-cigarette e-commerce e-learning S-hook T-shirt U-turn 1,2-dimethylbutylene 2,4-D ...' [BtB Public Works ... Translation Bureau] – Edwin Ashworth Aug 07 '21 at 10:59
  • Thanks, but no. t-distribution refers to a compound thing, so there must be a hyphen. This is different with the question (or is it?). – null Aug 07 '21 at 11:00
  • Yes it does, within the remit of ELU. [n times] or [n-times] is a compound word with a letter as first element, as are 'T-shirt' and 'e-commerce'. If there is here (as DjinTonic's research shows) a very different bias, this is because of the mathematical preferences involved, and this question is better asked on Mathematics.SE. Lexico gives the hyphenated spelling of the adjective two-time: [adj] [attributive] ... ‘a two-time winner of the event’. (Though I'm sure the open compound is also used.) – Edwin Ashworth Aug 07 '21 at 11:23
  • @EdwinAshworth I've edited my answer. I believe two-time and two times/two-times behave differently. Few would disagree with the hyphen for time. – DjinTonic Aug 07 '21 at 12:02
  • @DjinTonic Probably. 'Two-time' is on-topic (if answerable by basic research); 'n-times / n times' (prenominal) as used here is non-everyday English, I'd say maths-specific. – Edwin Ashworth Aug 07 '21 at 14:07
  • @EdwinAshworth Even if n times is based on analogy with four times champion of the world? – DjinTonic Aug 07 '21 at 14:12
  • @DjinTonic 'No hyphen seems to be much more common' seems to need 'in maths usages': a Google search for "four times champion" rather than "four times differentiable" gives a less uneven distribution of hyphenated/open forms. Of course, it's hard to find an everyday adjective that 'n times' modifies sensibly. – Edwin Ashworth Aug 07 '21 at 14:28
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    @EdwinAshworth Edited. – DjinTonic Aug 07 '21 at 14:33

2 Answers2

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No hyphen seems to be much more common in math, as this Google Books search for "N-times differentiable function" indicates, with six out of six examples hyphenless. (Looking at more pages in the search I see one example with a hyphen and dozens without.) If I were writing this, my instinct would be to use a hyphen.

This may have to do with how we modify times:

"...and will meet with n times as many ethereal particles , and will impinge upon each particle with n times greater velocity" ref

...the lifting force becomes n times greater than it was... ref

I think we agree that a hyphen is needed for a six-time Olympic champion.

However,

... making her a four times champion of the world. ref (1918)

and

...he was not destined to join Harry Vardon and Braid as four-times champion ref (1908)

DjinTonic
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  • Yes, I feel it more natural to use hyphen, though I don't why the literature go without hyphen. – null Aug 07 '21 at 11:09
  • 1,2-dimethylbutylene is prescribed. And Lexico gives the hyphenated spelling of the adjective two-time: [adj] [attributive] Denoting someone who has done or experienced something twice. ‘a two-time winner of the event’. This question is thus obviously about non-quotidian English usage; this belongs on Mathematics. – Edwin Ashworth Aug 07 '21 at 11:21
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I would write it as

n–times differentiable function

Why the en-dash?

Because n and times are compound adjectives describing function. It makes no sense to say

? n function

or

? times function;

both the n and the times must be modifying function together to make sense.

Here are some helpful citations:

Student t-distribution: why the dash [sic, EA; hyphen]

When should com­pound words be writ­ten as one word, with hy­phens, or with spaces?

Why is n lowercase?

When n refers to an arbitrary integer in writing about mathematics, it is written in lowercase and (usually) is italicized (and put into a math font).

rajah9
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