# Independence (disambiguation)

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In business, an independent business is a term of distinction and is generally used to refer to businesses which are privately owned as opposed to those publicly owned through a distribution of shares on the market. A sole-proprietorship is the most common form of independent business. Other terms of distinction used in addition to independent businesses are small business and startup business, which have varying subtleties of distinction.

## Religion

In English church history, Independents advocated local congregational control of religious and church matters, without any wider geographical hierarchy, either ecclesiastical or political. Independents reached particular prominence between 1642 and 1660, in the period of the English Civil War and of the Commonwealth and Protectorate, wherein the Parliamentary Army became the champion of Independent religious views against the Anglicanism or the Catholicism of Royalists and the Presbyterianism favoured by Parliament itself.

## Mathematics

The term independent is used with a variety of distinct meanings in mathematics.

P(X <s, Y<t)=P(x<s)P(Y<t). Intuitively speaking, this means that the observed size of X as no influence on the probability law for Y, and conversely.

• A set of vectors is said to be linearly independent provided that the only representation of zero as a linear combination of these vectors is the trivial combination where each vector is multiplied by zero. If every element of a space S can be written a linear combination of the set of given vectors, those vectors are said to span S. A collection independent vectors that span S is said to be a basis for S. For example, the vectors (1,0,0), (0,1,0), and (0,0,1) are linearly independent, and they form a basis for three-dimensional Euclidian space.
• The argument to a function often called the independent variable. This is an entirely different concept from those of statistical independence or linear algebraic independence.
• A proposition P is said to logically independent of a set of axioms A, provided that there exists a consistent mathematical model where the proposition P and the axioms of A are true, and also there exists a consistent model where "not P" and the axioms of A are true. Intuitively, this means that in a world where the axioms in A are true, you would not get a contradiction by also assuming that P is true, and, analogously, you would not get a contradiction if you assume that P is false.

P.J. Cohen proved that the "contiuum hypothesis" concerning the cardinality of the set of real numbers is a proposition that is independent of the usual model for arithmetic. This settled problem number 1 on David Hilbert famous list of mathematical problems.

References:

P. J. Cohen, Independence of the Continuum Hypothesis

S. Lange Linear Algebra

W. Feller Introduction to Probability Theory, volume I.

## Politics

Independence is the status of a state or country whose government is not subject to any other government. In the Eastern Orthodox Church, a similar concept is called autocephaly.

In politics, an independent is a voter or a politician who is not affiliated with any political party. In countries with a two-party system, independents may hold a centrist viewpoint between the two parties, or may feel that neither of the two parties adequately represents their viewpoint.

Recent independent candidates for U.S. President include John Anderson in 1980, Ross Perot in 1992 and Ralph Nader in 2004.

## Newspaper

The Independent is a British broadsheet newspaper, first published in 1986.

## Film

An independent film (or indie film) is a film produced without the support of a major movie studio or a big budget.

## Music industry

In the music industry, an independent record label -- or indie -- is a record label not associated with the 'major' record labels.

## Professional Wrestling

In Professional wrestling, an independent promotion -- or "indy" -- is a wrestling show not associated with the 'major' wrestling promotions.

## Aviation

In aviation, Independence Air is the name of a low-cost airline.

## Places in the United States

zh:独立

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