You want to assert that every case holds, by ruling out any single exception.
序 · The move
1open with 沒有 to deny that an exception existsis the outer 沒有 a denial of existence, not a denial of possession on the subject?
2narrow to a single case with 一 + measure (一個, 一首, 一次)is it one single unit, not a plural amount?
3deny the predicate inside with 不 (will/quality/habit) or 沒 (completed/experience)does the inner negator match the predicate's aspect, and is it present? drop it and the claim flips to 'no such case exists at all'
4close with 的 to settle it as factdoes the sentence end on 的, sealing the whole double negation?
例 · Examples
1來過這間餐廳用餐的seals it as settled fact顧客，沒有there is not (denies any such case exists)一個one (single unit: a single customer)不說好does not praise (inner denial)的。哥哥很喜歡這位歌手，沒有一首one (single unit: a single song)歌他沒聽過has not heard (inner denial, completed/experience)的。
Of the customers who have eaten at this restaurant, there isn't one who doesn't praise it. My brother loves this singer; there isn't a single song of his he hasn't heard.
界 · Boundary
一…都/也+不/沒…
一…都/也…不/沒… is a single negation that sweeps the floor case OUT — not even one holds (none). 沒有一…不/沒…的 stacks two negations that cancel and sweep every case IN — not one fails to hold (all). The outer 沒有 plus 的 is what turns the denial into a universal claim.
Plain 沒有 denies a thing is held or is there (沒有一個人 = there is no one). Add an inner 不/沒 and a closing 的 and the same 沒有 reverses: 沒有一個人不來 = there is no one who doesn't come = everyone comes. The inner negator is what flips absence into totality.
dropping the inner negator (reads as plain absence, not totality): 沒有一個說好的 (no one praises it) → 沒有一個不說好的 (everyone praises it)
inner aspect mismatch: 沒有一首歌他不聽過的 → 沒有一首歌他沒聽過的 (experience calls for 沒)
omitting the closing 的: 沒有一個不說好 → 沒有一個不說好的
English 'there isn't one who doesn't…' is grammatical but rare, so learners avoid the double negative and reach for a plain 'everyone…' (每個都…); they also drop the inner 不/沒 or the closing 的, collapsing the totality back to plain absence.