Hm... The wiki says we want to use "nonempty" for sets that are not empty:

I haven't noticed that rule when making my edit. It's surprising to me, because there are 18 uses of non-empty in the standard, and only 5 uses of nonempty, so I thought of it as an obvious inconsistency that can be fixed. You can even find two occurrences of non-empty set.

Empty is also a C++ term for strings at least, defined in [byte.strings], so doesn't it arguably fall under the first bullet in the wiki? At least it should for the change in [lex.phases] I've made.

The wiki also mentions nonempty as an example of a well-established non-hyphenated form. However, Google Trends suggests that non-empty is significantly more common, and I can't find any authoritative source that recommends nonempty. Overall, non-empty is more popular in the C++ standard and elsewhere.

Maybe the wiki should be updated, since its recommendation doesn't match common practice in the standard, or common practice elsewhere.

#440 was reopened for this.