Almost all

In mathematics, the phrase "almost all" has a number of specialised uses which extend its intuitive meaning.

Cardinality

"Almost all" is sometimes used synonymously with "all but [except] finitely many" (formally, a cofinite set) or "all but a countable set" (formally, a cocountable set); see almost.

A simple example is that almost all prime numbers are odd, which is based on the fact that all but one prime number are odd. (The exception is the number 2, which is prime but not odd.)

Measure theory

When speaking about the reals, sometimes it means "all reals but a set of Lebesgue measure zero" (formally, almost everywhere). In this sense almost all reals are not a member of the Cantor set even though the Cantor set is uncountable.

More generally, "almost all" is sometimes used in the sense of "almost everywhere" in measure theory, or in the closely related sense of "almost surely" in probability theory.

Number theory

In number theory, if P(n) is a property of positive integers, and if p(N) denotes the number of positive integers n less than N for which P(n) holds, and if

Direct-to-video

Direct-to-video or straight-to-video (also known as direct-to-VHS, direct-to-DVD, direct-to-Blu-ray, direct-to-digital, etc.) refers to the release of a film to the public immediately on home video formats rather than a theatrical release or television broadcast. Because inferior sequels or prequels of larger-budget films may be released direct to video, references to direct-to-video releases are often pejorative. However, this belief is changing, with direct-to-video releases having become something of a profitable lifeline for independent filmmakers and smaller companies.

Reasons for releasing direct to video

A production studio may decide not to generally release a TV show or film for several possible reasons: a low budget, lack of support from a TV network, negative reviews, its controversial nature, or a simple lack of general public interest. Studios, limited in the annual number of films to which they grant cinematic releases, may choose to pull the completed film from the theaters, or never exhibit it in theaters at all. Studios then generate revenue through video sales and rentals.