Etymology
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Words related to *ne-

a- (3)
prefix meaning "not, without," from Greek a-, an- "not" (the "alpha privative"), from PIE root *ne- "not" (source also of English un-).

In words from Greek, such as abysmal, adamant, amethyst; also partly nativized as a prefix of negation (asexual, amoral, agnostic). The ancient alpha privatum, denoting want or absence.

Greek also had an alpha copulativum, a- or ha-, expressing union or likeness, which is the a- expressing "together" in acolyte, acoustic, Adelphi, etc. It is from PIE root *sem- (1) "one; as one, together with."
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abnegate (v.)
Origin and meaning of abnegate
"deny (something) to oneself," 1650s, from Latin abnegatus, past participle of abnegare "to refuse, deny," from ab "off, away from" (see ab-) + negare "to deny," from PIE root *ne- "not." Related: Abnegated; abnegating.
ahimsa (n.)
doctrine of non-violence, 1875, from Sanskrit ahimsa, from a "without" (from PIE root *ne- "not") + himsa "injury."
an- (1)
privative prefix, from Greek an-, "not, without," from PIE root *ne- "not"). The Greek prefix is a fuller form of the one represented in English by a- (3).
annihilate (v.)
"reduce to nothing," 1520s, from Medieval Latin annihilatus, past participle of annihilare "reduce to nothing," from Latin ad "to" (see ad-) + nihil "nothing" (see nil). Related: Annihilated; annihilating.

Middle English had a past-participle adjective annichilate "destroyed, annulled, reduced to nothing" (late 14c.), from past participle of Old French anichiler "annihilate, destroy" (14c.) or the Medieval Latin verb.
annul (v.)
late 14c., "invalidate, make void, nullify;" from Anglo-French and Old French anuler "cancel, wipe out" (13c.) or directly from Late Latin annullare "to make to nothing," from Latin ad "to" (see ad-) + nullum, neuter of nullus "nothing, none," from PIE root *ne- "not." Related: Annulled; annulling.
aught (n.2)
"nothing, zero," faulty separation of a naught (see naught). See adder for similar misdivisions.
deny (v.)

early 14c., "declare to be untrue or untenable," from Old French denoiir "deny, repudiate, withhold," from Latin denegare "to deny, reject, refuse" (source of Italian dinegarre, Spanish denegar), from de "away" (see de-) + negare "refuse, say 'no,' " from Old Latin nec "not," from Italic base *nek- "not," from PIE root *ne- "not."

From late 14c. as "refuse, refuse to grant or give," also "refuse to acknowledge, disavow, disown." Sense of "refuse access to" is from 1660s. Related: Denied; denying.

I may not understand what you say, but I'll defend to your death my right to deny it. [Albert Alligator, "Pogo," Sept. 26, 1951] 
hobnob (v.)
1763, "to drink to each other," from hob and nob (1756) "to toast each other by turns, to buy alternate rounds of drinks," alteration of hab nab "to have or have not, hit or miss" (c. 1550), which is probably ultimately from Old English habban, nabban "have, not have," (that is, "to take or not take," used later as an invitation to drinking), with the negative particle ne- attached (from PIE root *ne- "not"), as was customary; see have. Modern sense of "socialize" is 1866. Related: Hobnobbed; hobnobbing.
in- (1)
Origin and meaning of in-
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.