Can “non” be used as a separate word?

Question

I used non trivial and a grammar correction website shows it is wrong and should be either non-trivial or nontrivial.

1. x appears in a non trivial number of pages

Or

2. x appears in a non-trivial number of pages

Or

3. x appears in a nontrivial number of pages

Answer 1

The correct spelling is either non-trivial or nontrivial. (British writers tend to prefer the hyphenated form)

"Non" is not used as an independent word, it may be a prefix or it can be written hyphenated. An independent word "non" is used in some Latin phrases eg non compos mentis (meaning "not of sound mind"). This is discussed in the wiktionary usage notes

Answer 2

I agree with your grammar checker. "Non-" is a prefix, not a separate word. It can either be fully attached to the word it modifies, or attached with a hyphen.

"Not" can often be used as a separate word instead of "non-".

The following example #4 is technically acceptable, but is not as natural as any of examples 2, 3, and 5. Examples 2 and 3 are more natural than example #5:

4. x appears in a not trivial number of pages

5. The number of pages that x appears in is not trivial.