What separates なき from なし？


E.G. お忘れなき ＆ 迷いなし

I know they're both ways to end a a sentence, but I never could figure what
make each different from the other. Anyone have a clue?




The answer in terms of classical Japanese is probably what you're looking for,
as the modern usage will be -based- on its proper classical usage, but
basically なき is 連体形 and なし is 終止形. In modern Japanese the distinction between
連体形 and 終止形 has deteriorated, but if I were to stress a distinction, 連体形
functions in modern Japanese (when it is -not- attaching to a noun) as if it
has an explanatory/declarative の/もの/こと at the end. In modern Japanese, that
"explanatory の particle" you learn is just a marker to make clear the
preceding verb is in its 連体形 form (though this の is not always necessary).

This is -partially- due to the remnants of the 係り結び bound-particles system,
and is also similar to why sentences can end in both か and のか (though they
both have to be in the 連体形 technically), which started degrading even before
we really hit modern Japanese. One other way of putting it is that -because-
the ending is 連体形 and not 終止形 it implies that something that is supposed to
follow was omitted.

お忘れなき on its own is basically: お忘れ（は）ないこと. I'd say it's closest to
"お忘れ（し・は）ないようにね"

迷いなし is simply a statement. 迷い(は)ない. Depending on context this could be "I am
not lost/hesitating etc." basically to mean "All's fine here."

Hope that helps.

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Since we were talking about it in the comments I'll add another usage of なし.
終止形 can be used for nominalization and なし is a common case that forms (adj-no)
"adjective-type noun" when used for nominalization. In this case it acts like
an na-adjective but uses の instead of な (because it is technically a noun, not
an adjective).

A very common example is the word: なけなし. "なけなしのお金" - a small amount ("not no")
of money.

Other examples given by snailboat include: 「ネクタイなしの軽装」「文句なしだ」「アスプリン・砂糖なしの錠剤」

If I were to say there were a difference between 文句なし and 文句なしだ... The former
is simply "there are no complaints" and the latter is "(in describing the
situation you have referred to/we are talking about) there are no complaints".
An insignificant nuance by itself, but using the だ would be more appropriate
when tying it in with a larger sentence structure. "前のことについてなんですけど、それは文句なしだ。"

--

The difference between べき・べし works similarly, just with more irregularities,
because べき itself is treated as a na-adj nowadays.

