Everything in life has a negative side to it. This nasty fact has also left its mark on language, in the form of negative prefixes that will turn just everything into its opposite. Or spoil it some other way, by contradicting, denying, canceling, revoking or refuting it. Like English "un-" and" "in-," "dis-" and "de-," "non" and "no-," Japanese has a number of forms that do this destructive job. And they do it quite well.
The most neutral negative prefix is 無 (mu, bu), used first and foremost to indicate the absence or lack of something. A figurative example is 無人島 (mujintō), a "no-people island" — that is, one that is uninhabited. Likely more familiar to city-dwellers is the term 年中無休 (nenchū mukyū, open 24/7 year-round), where 無 indicates the absence of holidays through the year.
Despite its negating function, 無 can generate quite positive expressions. In the world of money, for instance, it brings us consumer-friendly concepts like 無料 (muryō, free of charge) and 無税 (muzei, tax-free). And just as drivers aspire to a spotless record of no accident and no traffic violations (無事故無違反, mujiko muihan), goalkeepers try to keep a clean sheet (無失点, mushitten). The positive potential of negative 無 is perhaps best captured in the term 無事 (buji, literally "without a thing"), referring to all manner of states of safe-and-soundness.