Etymology
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Words related to a-

*ne- 
Proto-Indo-European root meaning "not."

It forms all or part of: a- (3) "not, without;" abnegate; ahimsa; an- (1) privative prefix; annihilate; annul; aught (n.2) "zero, nothing;" deny; hobnob; in- (1) "not, opposite of, without;" ixnay; naught; naughty; nay; nefarious; negate; neglect; negligee; negotiate; neither; nepenthe; nescience; nescient; neuter; never; nice; nihilism; nihility; nil; nill; nimiety; nix; no; non-; none; nonplus; nor; not; nothing; null; nullify; nulliparous; renegade; renege; un- (1) prefix of negation; willy-nilly.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit a-, an- "not;" Avestan na "not;" Greek a-, an-, ne- "not;" Latin in- "not," ne "that not;" Old Church Slavonic and Lithuanian ne "not;" Old Irish an-, ni, Cornish ny "not;" Gothic and Old English un- "not."
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un- (1)

prefix of negation, Old English un-, from Proto-Germanic *un- (source also of Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), combining form of PIE root *ne- "not." Often euphemistic (such as untruth for "lie").

The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.

It also makes words from phrases (such as uncalled-for, c. 1600; undreamed-of, 1630s; uncome-at-able, 1690s; unputdownable, 1947, of a book; un-in-one-breath-utterable, Ben Jonson; etc., but the habit is not restricted to un-; such as put-up-able-with, 1812). As a prefix in telegramese to replace not and save the cost of a word, it is attested by 1936.

abysmal (adj.)

1650s, "pertaining to an abyss," formed in English from abysm + -al (1). Perhaps only a dictionary word before 19c. The weakened sense of "extremely bad" is attested by 1904, perhaps from abysmal ignorance (suggestive of its "depth"), an expression attested from 1847. Related: Abysmally.

adamant (adj.)

late 14c., "hard, unbreakable," from adamant (n.). The figurative sense of "unshakeable" (in belief, etc.) is by 1670s. Related: Adamantly; adamance.

amethyst (n.)

violet-colored quartz, late 13c., amatist, from Old French ametiste (12c., Modern French améthyste) and directly from Medieval Latin amatistus, from Latin amethystus, from Greek amethystos "amethyst," noun use of an adjective meaning "not intoxicating; not drunken," from a- "not" (see a- (3)) + methyskein "make drunk," from methys "wine" (from PIE root *medhu- "honey; mead;" see mead (n.1)).

The stone had a reputation among the ancients for preventing drunkenness; this was perhaps sympathetic magic suggested by its wine-like color. Beekes writes that the stone "was named after its color: the red of wine diluted with water such that it is no longer intoxicating." When drinking, people wore rings made of it to ward off the effects. The spelling was restored in early Modern English.

asexual (adj.)
1829, as a term in biology, "having no sex or sexual system," a hybrid from a- (3) "not" + sexual. In general contexts, "wanting sexuality, being of or referring to neither sex," attested from 1896.
amoral (adj.)

"ethically indifferent," 1882, a hybrid formed from Greek-derived a- "not" (see a- (3)) + moral, which is from Latin. Apparently coined by Robert Louis Stevenson as a differentiation from immoral.

agnostic (n.)

1870, "one who professes that the existence of a First Cause and the essential nature of things are not and cannot be known" [Klein]; coined by T.H. Huxley, supposedly in September 1869, from Greek agnostos "unknown, unknowable," from a- "not" (see a- (3)) + gnōstos "(to be) known" (from PIE root *gno- "to know"). The coinage is sometimes said to be a reference to Paul's mention of the altar to "the Unknown God" in Acts, but according to Huxley it was a reference to the early Church movement known as Gnosticism (see Gnostic). The adjective also is from 1870.

I ... invented what I conceived to be the appropriate title of 'agnostic,' ... antithetic to the 'Gnostic' of Church history who professed to know so much about the very things of which I was ignorant. [T.H. Huxley, "Science and Christian Tradition," 1889]
The agnostic does not simply say, "I do not know." He goes another step, and he says, with great emphasis, that you do not know. [Robert G. Ingersoll, "Reply to Dr. Lyman Abbott," 1890]
acolyte (n.)
Origin and meaning of acolyte

early 14c., "inferior officer in the church," from Old French acolite or directly from Medieval Latin acolytus (Late Latin acoluthus), from Greek akolouthos "following, attending on," as a noun, "a follower, attendant," literally "having one way," from a- "together with," copulative prefix (see a- (3)), + keleuthos "a way, road, path, course, journey," which is of unknown etymology. The word was in late Old English as acolitus, a Latin form; in early modern English a corrected form acolythe was used.

acoustic (adj.)

c. 1600, "pertaining to hearing or sound," from French acoustique, from Latinized form of Greek akoustikos "pertaining to hearing," from akoustos "heard, audible," verbal adjective from akouein "to hear," which probably is from copulative prefix a- (see a- (3)) + koein "to mark, perceive, hear" (from PIE root *kous- "to hear," which is also the presumed source of English hear).

In reference to material meant to deaden sound, 1924. Of sound reproduced mechanically (rather than electrically) from 1932 in reference to gramophone players; acoustic guitar (as distinguished from electric) is attested by 1958. Related: Acoustical; acoustically.