a prefix used freely in English and meaning "not, lack of," or "sham," giving a negative sense to any word, 14c., from Anglo-French noun-, from Old French non-, from Latin non "not, by no means, not at all, not a," from Old Latin noenum "not one" (*ne oinom, from PIE root *ne- "not" + PIE root *oi-no- "one, unique"). In some cases perhaps from Middle English non "not" (adj.), from Old English nan (see not). "It differs from un- in that it denotes mere negation or absence of the thing or quality, while un- often denotes the opposite of the thing or quality" [Century Dictionary].
"existing, having existence," 1560s, a back-formation from existence, or else from Latin existentem/exsistentem (nominative existens/exsistens), present participle of existere/exsistere "to exist, be" (see existence).
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Harper, D. (n.d.). Etymology of non-existent. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/non-existent