TITLE: Math terminology: What are rules regarding hyphens? (Nonzero vs. non-zero)
QUESTION [11 upvotes]: 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.

REPLY [2 votes]: 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