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.