Axiom

An axiom or postulate as defined in classic philosophy, is a statement (in mathematics often shown in symbolic form) that is so evident or well-established, that it is accepted without controversy or question. Thus, the axiom can be used as the premise or starting point for further reasoning or arguments, usually in logic or in mathematics The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'

As used in modern logic, an axiom is simply a premise or starting point for reasoning. Whether it is meaningful (and, if so, what it means) for an axiom, or any mathematical statement, to be "true" is a central question in the philosophy of mathematics, with modern mathematicians holding a multitude of different opinions.

As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define (e.g., (A and B) implies A), while non-logical axioms (e.g., a + b = b + a) are actually substantive assertions about the elements of the domain of a specific mathematical theory (such as arithmetic). When used in the latter sense, "axiom", "postulate", and "assumption" may be used interchangeably. In general, a non-logical axiom is not a self-evident truth, but rather a formal logical expression used in deduction to build a mathematical theory. As modern mathematics admits multiple, equally "true" systems of logic, precisely the same thing must be said for logical axioms - they both define and are specific to the particular system of logic that is being invoked. To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain.

Axiom (computer algebra system)

Axiom is a free, general-purpose computer algebra system. It consists of an interpreter environment, a compiler and a library, which defines a strongly typed, mathematically (mostly) correct type hierarchy.

History

Two computer algebra systems named Scratchpad were developed by IBM. The first one was started in 1965 by James Greismer at the request of Ralph Gomory, and written in Fortran. The development of this software was stopped before any public release. The second Scratchpad, originally named Scratchpad II, was developed from 1977 on, at Thomas J. Watson Research Center, under the direction of Richard Dimick Jenks. Other key early developers were Barry Trager, Stephen Watt, James Davenport, Robert Sutor, and Scott Morrison.

Scratchpad II was renamed Axiom when IBM decided, circa 1990, to make it a commercial product. A few years later, it was sold to NAG. In 2001, it was withdrawn from the market and re-released under the Modified BSD License. Since then, the project's lead developer has been Tim Daly.

Axiom (album)

Axiom is the ninth studio album by the London-based trip hop band Archive. It was released in May 2014.

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Charts

References

Hades (film)

Hades is a 1995 German drama film directed by and starring Herbert Achternbusch. It was entered into the 45th Berlin International Film Festival.

Cast

References

External links

Hades (rapper)

Łukasz Bułat-Mironowicz (born 16 August 1985), better known by his stage name Hades, is a Polish rapper. He is also member of bands HiFi Banda and RH-.

Discography

Studio albums

Music videos

References

Sinope (moon)

Sinope (/sᵻˈnoʊpiː/ sə-NOH-pee;Greek: Σινώπη) is a retrograde irregular satellite of Jupiter discovered by Seth Barnes Nicholson at Lick Observatory in 1914, and is named after Sinope of Greek mythology.

Sinope did not receive its present name until 1975; before then, it was simply known as Jupiter IX. It was sometimes called "Hades" between 1955 and 1975.

Sinope was the outermost known moon of Jupiter until the discovery of Megaclite in 2000. The most distant moon of Jupiter now known is S/2003 J 2.

Orbit

Sinope orbits Jupiter on a high eccentricity and high inclination retrograde orbit. The orbital elements are as of January 2000. They are continuously changing due to solar and planetary perturbations. It is often believed to belong to the Pasiphae group. However, given its mean inclination and different colour, Sinope could be also an independent object, captured independently, unrelated to the collision and break-up at the origin of the group. The diagram illustrates Sinope's orbital elements in relation to other satellites of the group.