word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
late 14c., "foresight, prudent anticipation, timely care or preparation," from Old French providence "divine providence, foresight" (12c.) and directly from Latin providentia "foresight, precaution, foreknowledge," abstract noun from present-participle stem of providere "look ahead, prepare, supply, act with foresight," which is from pro "ahead" (see pro-) + videre "to see" (from PIE root *weid- "to see").
Providence (usually capitalized) "God as beneficent caretaker of his creatures," is recorded c. 1600, from earlier use of the word for "God's beneficent care, guardianship, or guidance" (late 14c., short for divine providence, etc.). The noun in classical Latin occasionally was used as the name of a goddess and in Late Latin as "God; the government of the world by God's infinite wisdom and foresight."
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Harper, D. (n.d.). Etymology of improvidence. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/improvidence