The prefix a- is used in Greek to express absence or negation. For example, gamos means "married" and agamos means "unmarried." Before a vowel, the a- becomes an-. Isos means "even," so anisos will mean "uneven" and thus, by extension, "unjust" or "unfair."

The alpha privative serves the same function in Greek as the prefix un- does in English, and in fact is believed to come from the same proto-Indo-European root (vocalized *M-). The equivalent in Latin is im- or in-.

Alpha privatives are occasionally found in English words that have been borrowed from Greek. Thus a theist is a person who believes in a God, while an atheist is a person who does not. Someone who is apathetic feels no pathos, or passion. An anarchist is someone who is not interested in having an archos, which is to say a ruler.

Latin borrowings into English are usually negated with the Latin prefixes (which are also sometimes called alpha privatives even though there is no alpha involved). Therefore someone who is not moral is immoral, something that is not active is inactive, something that is not perfect is imperfect, and so on.

As Martin Heidegger was fond of pointing out, the Greek word for truth, aletheia, contains an alpha privative. Lethe is the mythical river of forgetting (from lanthano, to be concealed, to escape notice). Hence, truth for the Greeks was an un-forgetting or an un-hiding of something that was always there.

Needless to say, not all a-'s and an-'s and im-'s and in-'s are alpha privatives. The common Greek prefix ana- means, among other things, "up" or "away" -- an anathema, then, is a setting apart of something, not a denial of it. Similarly, the Latin prefix in- can be translated with the English preposition "in" in certain cases. Inter- can be translated with "between." So you'll look kind of foolish if you try to argue that "infestation" means "not fested," or that "interaction" means "lack of teraction."