The English words 'no' and 'no' don't share a common ancestor. 'No', the opposite of 'yes', comes from Proto-West-Germanic *naiw (never), while 'no' as in 'no pain, no gain' comes from *nain (not any): it arose as a variant of 'none'.
'No' as opposed to 'yes' isn't related to German 'nein' and Dutch 'nee' either. Their only common part is 'n-', which comes from the Germanic negation particle *ne, also found in words such as 'not', 'neither' and 'never'.
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@yvanspijk But no and no both come from Proto-Germanic ne ? So ne splits to naiw and nain which end up as no no?
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@ppscrv As the infographic shows, *ne was only one of the two ingredients of *naiwaz and *nainaz. The other ingrediënts were *aiwaz and *ainaz. It's like the words 'forget' and 'forgive', which both contain the element 'for-'.
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@yvanspijk But is like Mr X has children with Ms A and with Ms B. Mr X would still be a common ancestor to Ms A's and Ms B's descendents. I think. But that is not how it works elements of language?
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@ppscrv No, doesn't work like that in languages, because that would mean that all English words starting with 'un-' ('unravel', 'unwind' etc.) would have the same origin too. What's important is the stem, and even then, 'to forget' and 'to beget' are certainly related, but they don't have the same origin; all we can say is they're both derivatives of 'to get'.
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@yvanspijk I see. I think. Perhaps it looks tricky because ne and no are so short. And ne is possibly not even a stem at all.
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