Math terminology: What are rules regarding hyphens? (Nonzero vs. non-zero)

Question

This question is geared toward clarifying terminology in writing math.

Which terms are correct and why?

A set $E$ is non-empty.
A set $E$ is nonempty.

The number $x$ is non-negative.
The number $x$ is nonnegative.

The number $y$ is non-positive.
The number $y$ is nonpositive.

The number $z$ is non-zero.
The number $z$ is nonzero.

As a personal preference, I like the way nonzero looks but I prefer to use non-empty so I don't know what the consistency with hyphens is when prefixing "non". I also like the way nonnegative reads but I feel like non-positive looks better than without a hyphen. I don't have any rhyme or reason why I have these preferences and that's why I'm curious to learn if there is a correct version of each term listed above.

This would be more suitable on http://english.stackexchange.com/ as the word-formation rules probably don't have much to do with actual math. — the gods from engineering, Feb 07 '15 at 18:26
I'd be surprised if the technicality of the terms is relevant to answer this question. Have you tried asking at English Language S.E. or English Language Learners S.E.? — Git Gud, Feb 07 '15 at 18:26
@RespawnedFluff I considered that SE but I figured that mathematicians would have more familiarity seeing these terms and have a better sense of which one is more common or be able to give reasons why they prefer/avoid hyphens. — Xoque55, Feb 07 '15 at 18:29
I'll just do whatever that pleases the spell checker I'm using and concentrate on the real math. Only when it get to the point to get something published, you ask your secretary or English major friend for proof reading. — achille hui, Feb 07 '15 at 18:34
Maybe someone can actually provide info if the major math publishing houses, like AMS, Springer etc., have any rules or preferences expressed in some style document of theirs. — the gods from engineering, Feb 07 '15 at 18:34
Both are generally accepted. I much prefer and always use the hyphenated versions. — Brian M. Scott, Feb 07 '15 at 20:38
I use hyphens before capital letters, so "non-Abelian" instead of "nonAbelian". — bof, May 19 '16 at 11:08
Relevant question on the English SE: Hyphens after the prefixes “non-” and “anti-” in mathematics — , Jun 18 '16 at 15:43
Once long ago, an AMS journal corrected "non-negtive" to "nonnegative" in a paper of mine, so I have used it (and similar spellings) ever since. — GEdgar, Jul 31 '16 at 23:38
My spellchecker underlines nonzero and suggests fixing it to non-zero. — Calmarius, Aug 21 '19 at 10:56
This link says it is better to write "nonempty", no hyphen or space: https://groups.google.com/forum/#!topic/misc.education.language.english/NiJJCBpGVRc — john c. j., May 12 '20 at 22:41

score 8 · Answer 1 · edited May 11 '22 at 05:58

Since many (or a nonnegligible amount) of authors just do not care, I guess it's up to personal preference. However, there is a semantic code, like pointed out here. Thereafter, the prefix non is not hyphenated. And I really think this should be consistent. I had nonzero, nonempty and nonholonomic occurring in my thesis and it was "corrected" by different supervisors into different versions, mostly where non-holonomic was hyphenated and the rest not. I really think this is bad practice, since consistency is lost by this "to highlight" mentality. If on tries to highlight something, why not explain it and treat it consistently in semantics.

To underline my point consider using $X$ for vectors in one direction. For some other vector, to hightlight that it's not in this direction you use $\alpha$. But why not $Y$ with an explanation?! Therefore, semantics is consistent and the highlights are where they belong, in the "comments".

What got me to enforce this was that every title I cited contained the nonhyphenated versions of all those words. Thus, (from a far too small sample, but of good works) I conclude that this is common practice in this field (between robotics and automation).

Oxford Dictionary also advises to use hyphens for prefixes, which lead to vowel collisions, like pre-advised, although nothing further is stated there.

I was stuck between languages and just wrote some mixture, what I meant was nonnegligible. — mike, May 19 '16 at 13:49

score 3 · Answer 2 · answered Jul 18 '20 at 01:32

3

Donald Knuth says we should drop the hyphens.

Here is the link to his post in which he says so:

https://cs.stanford.edu/~knuth/email.html

answered Jul 18 '20 at 01:32

Marvelous ! Not only because he writes about hyphens. – Kurt G. May 11 '22 at 08:53

score -1 · Answer 3 · answered Feb 07 '15 at 18:27

-1

In mathematics, it is usual to formulate above words without hyphens. Some People want to clarify difficult words by separating These with Hyphens; so words with Hyphen arise.

answered Feb 07 '15 at 18:27

kryomaxim

2,882

5

If I search in Google Books "non-negative" vs. "nonnegative" they're about tied, and the top hits are all math books for both searches. – the gods from engineering Feb 07 '15 at 18:28

Anthony · Answer 4 · 2022-05-12T13:34:20.223

-3

It seems that positive is better word usage than "nonnegative" or "non-negative"? Also should it be not equal to zero as opposed to "nonzero" or 'non-zero"?

Update: I was surprised to find this has actually been discussed on Wikipedia: https://en.wikipedia.org/wiki/Parity_of_zero

edited May 12 '22 at 13:34

answered Oct 13 '16 at 12:10

Anthony

3,738

8

Positive and nonnegative are not the same though, as 'nonnegative' implies zero or positive, while 'positive' only implies positive. – T. Eskin Oct 13 '16 at 12:13
I did not know this. I have always taken zero to be a positive whole even number. – Anthony Oct 13 '16 at 12:15
3

@AntonioHernandezMaquivar This is just a convention. In French positive also includes zero, and I suppose the same holds for Spanish? – Roberto Rastapopoulos Feb 18 '19 at 18:23
@RobertoRastapopoulos I was taught that in school, yes. Is there a sound mathematical reason why $0$ would not be a positive number ? – Anthony Jun 03 '19 at 12:36
It is not about mathematical reasoning, it is about a convention. That said, the distinction between positive and nonnegative is more convenient than a distinction between positive and positive-but-not-0 – FShrike May 11 '22 at 07:25

Math terminology: What are rules regarding hyphens? (Nonzero vs. non-zero)

4 Answers4