Maybe this question is stupid, but I came to wonder:
Why do all negating words start with the letter n?
This is the case in all languages I know of.
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As John Lawler has indicated in a comment, most negating words in Indo-European languages derive ultimately from the root *ne-.
In non-IE languages, negative words take other forms, eg Hebrew לֺא (lo' = "not") or אין ('eyn' = "there isn't") or Turkish yok ("there isn't") or Georgian არ (ar = "not").
And even in IE languages, there are exceptions which have arisen in other ways, eg French pas, ("not", "none") Welsh ddim (ditto), Danish ikke, ("not").
There is more to "a particle that negates or inverts the value of the stem of the word" than just the letter n.
The concept is dealt with in some detail on Wikipedia, mainly under:
In Ancient Greek grammar, privative a (also known as privative alpha; in Latin, α prīvātīvum, in Greek, α στερητικόν) is the prefix a- that expresses negation or absence (e.g., a-theos, a-typical). It is derived from a Proto-Indo-European syllabic nasal *n̥- , the zero ablaut grade of the negation *ne, i.e. /n/ used as a vowel. For this reason, it appears as an- before vowels (e.g. an-alphabetism, an-esthesia, an-archy).1 It shares the same root with the Greek prefix nē or ne, in Greek νη or νε, that is also privative (e.g. ne-penthe).