"incapable of erring," 1610s, from Late Latin inerrabilis "unerring," from in- "not, opposite of" (see in- (1)) + errabilis, from Latin errare "to wander; to err" (see err). Related: Inerrability "infallibility" (1620s).
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.
c. 1300, from Old French errer "go astray, lose one's way; make a mistake; transgress," from Latin errare "wander, go astray," figuratively "be in error," from PIE root *ers- (1) "be in motion, wander around" (source also of Sanskrit arsati "flows;" Old English ierre "angry; straying;" Old Frisian ire "angry;" Old High German irri "angry," irron "astray;" Gothic airziþa "error; deception;" the Germanic words reflecting the notion of anger as a "straying" from normal composure). Related: Erred; erring.
<a href="https://www.etymonline.com/word/inerrable">Etymology of inerrable by etymonline</a>
Harper, D. (n.d.). Etymology of inerrable. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/inerrable