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Is the hyphen that we often see in words such as "non-zero", "non-trivial", etc. optional?

In case the answer is negative, is there any rule of thumb on which one may rely in order to recall when it is OK to leave it out?

Thanks in advance for your knowledgeable replies.

José Hdz. Stgo.
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    Almost every one of hundreds of words in the full OED starting with *non* is listed as a hyphenated form. A couple of exceptions that stood out to me when scrolling through them were the historical US noun *nonslaveholder* and adjectival / adverbial *nonverbal / nonverbally* (but for some reason they do actually hyphenate *non-verbalized*). So by far the best rule of thumb is to hyphenate in all cases. – FumbleFingers Aug 29 '18 at 17:20
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    @FumbleFingers is that a British thing or a quirk of the OED? I don't have access to it, but most other places I've checked show many of the non constructions without the dash. – Kevin Aug 29 '18 at 17:30
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    @Kevin: So far as I'm aware, the OED is *the* definitive English dictionary (they specifically identify AmE and BrE usages as such where relevant). In practice there's been an ongoing move towards using less "punctuation marks" in general over at least the past century, and if you ask me, BrE is less "conservative" than (post-Webster) AmE anyway.... – FumbleFingers Aug 29 '18 at 17:39
  • FWIW, ngrams show the non-hyphenated forms of your two examples have become more common since about 1960. Interestingly, if you look at AmE and BrE individually, in BrE the split was more like 1920, and the AmE split was much more pronounced in 1960. – Kevin Aug 29 '18 at 17:43
  • ... but if I compare BrE/AmE corpuses for *non-trivial, nontrivial* it seems that for Americans the two forms are at near-parity, but Brits overwhelmingly stick with the hyphenated version. So I guess there is a US/UK usage split, and I must admit it's not what I would have expected. – FumbleFingers Aug 29 '18 at 17:44
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    (Is that one of those "Jinx! You owe me a Coke!" moments? :) – FumbleFingers Aug 29 '18 at 17:45
  • Ha, yes. Just edged you out ;-) – Kevin Aug 29 '18 at 17:46
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    In any case, using the hyphen is never wrong, and is required in some cases. I'd say when in doubt use the hyphen, and only omit it if you memorize words that don't need it or look it up. – Kevin Aug 29 '18 at 17:48
  • Anyway, it's still the case that 3 out of 10 Americans are apparently happy to hyphenate *non-trivial, and it seems unlikely the other 7 would go so far as to say that's "incorrect" (as opposed to not being the stylistic choice they* would make). So I stand by the "rule of thumb" in my first comment, which I think should work perfectly well *both* sides of the pond. – FumbleFingers Aug 29 '18 at 17:51
  • (Jinx again! :) – FumbleFingers Aug 29 '18 at 17:51
  • @Kevin: While we are at it, is it a hyphen or a dash? An em-dash or an en-dash? – José Hdz. Stgo. Aug 29 '18 at 18:41
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    @JoséHdz.Stgo. a hyphen. You can see the usage here. A hyphen us used for compound constructions like "em-dash," em-dash is for separating phrases—like this—and en-dash is mostly for number ranges (e.g. 1949–57). – Kevin Aug 29 '18 at 18:54
  • Point taken ... – José Hdz. Stgo. Aug 29 '18 at 18:55
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    @FumbleFingers The problem I have with the OED in cases like these is that many of the pages haven't been updated since like 1989. And hyphenation can change faster than that. – Laurel Aug 29 '18 at 18:59
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    @Laurel As an official Canadian reference, I'm stuck with the second edition of the Canadian Oxford Dictionary which hasn't been updated since 2004. That's also too long a time for a dictionary to go without an update. – Jason Bassford Aug 29 '18 at 20:20

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To record and summarize the discussion in the comments, while the OED mostly uses the hyphen, many other dictionaries don't, and the ngrams show higher non-hyphenated usage than hyphenated.

Since using the hyphen is never wrong, and is preferred in some cases, when in doubt use the hyphen, and only omit it if you happen to know a word is commonly spelled without it.

And it's a true hyphen, not an en- or em-dash.

Kevin
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