* Formal definition of probability in the Mizar system, and the list of theorems formally proved about it.

When Mizar was found to be a binary, it was quite difficult to determine whether a double star was a binary system or only an optical double.

The system is maintained and developed by the Mizar Project under the direction of its founder Andrzej Trybulec.

Papers related to the Mizar system regularly appear in the peer-reviewed journals of the mathematic formalization academic community.

* If Alcor is considered part of the Mizar system, the system can be considered a sextuple.

* Mizar system

* The Mizar system, for writing mathematical definitions and proofs

The Mizar – Alcor stellar sextuple system consists of the quadruple system Mizar and the binary system Alcor.

Mizar ( Zeta Ursae Majoris, Zeta UMa, ζ Ursae Majoris, ζ UMa ) is a quadruple system of two binary stars in the constellation Ursa Major and is the second star from the end of the Big Dipper's handle.

As of 2007, the best estimates of Mizar and Alcor's respective distances place them 1. 1 light-years and 4 minutes of arc apart, and though their proper motions show they move together ( they are both members of the Ursa Major Moving Group ), it was long believed that they did not form a true binary star system, but simply a double star.

) that Alcor actually is itself a binary, consisting of Alcor A and Alcor B, and that this binary system is most likely gravitationally bound to Mizar, bringing the full count of stars in this complex system to six.

The distinctive feature of the Mizar language is its readability.

Mizar articles are written in ordinary ASCII, but the language was designed to be close enough to the mathematical vernacular that most mathematicians could read and understand Mizar articles without special training.

Distributions of the Mizar Proof Checker for all major operating systems are freely available for downloaded at the Mizar Project website.

The USS Mizar was built in 1932 for United Fruit Co. at Bethlehem Steel, Quincy, Massachusetts and originally named SS Quiriqua.

The SS Quiriqua was converted to the USS Mizar for Naval service by the addition of one single 5 "/ 38 caliber gun, four 3 "/ 50 caliber guns for anti-aircraft ( AA ) and anti submarine use and up to eight Oerlikon 20 mm cannon AA guns at Brewer's Drydock Co., Staten Island, N. Y.

Whenever Good / Phink morphs, Kat / Sludge morphs together ( although he is capable of doing it separated from his master, such as in the Saturn 500, when Phink says dogs aren't allowed on Mars and he morphs, causing Phink to says cats aren't either and in the Mizar Marathon when Good said that cats aren't allowed in a castle, to which he morphs and Good says that goes for dogs too ).

The band got its name after Mizar which is a guiding star for orientation of travelers in the deserts.

Beside influences such as Joy Division for instance, Mizar also uses elements of Traditional Macedonian folklore and Byzantine music.

Two years later the first two albums of Mizar were re-released on CD solely for the Macedonian market, but the record quickly spread across the countries of former Yugoslavia.

The Mizar Project was started around 1973 by Andrzej Trybulec as an attempt to reconstruct mathematical vernacular so it can be checked by a computer.

This is partly due to the complexity of mathematical notation, and partly to the limitations of existing theorem provers and proof assistants ; the paper finds that the major contenders, Mizar, HOL, and Coq, have serious shortcomings in their abilities to express mathematics.

Its current goal, apart from the continual development of the Mizar System, is the collaborative creation of a large library of formally verified proofs, covering most of the core of modern mathematics.

* Formalized Mathematics a journal in which Mizar proofs are presented.

The Mizar project has completely formalized and automatically checked the proof of the Hahn – Banach theorem in the HAHNBAN file.

While the Mizar proof checker remains proprietary, the Mizar Mathematical Library – the sizable body of formalized mathematics that it verified – is licensed open-source.

* Mizar – A proof assistant based on first-order logic, in a natural deduction style, and Tarski – Grothendieck set theory.

The second hunter ( Mizar ) carries a large pot — the star Alcor — on his shoulder in which to cook the bear while the third hunter ( Alkaid ) hauls a pile of firewood to light a fire beneath the pot.

The Mizar Mathematical Library ( MML ) includes all theorems which can be referred in newly written articles.

The most productive in the country was the post-punk, darkwave and gothic rock scene which included the cult bands Mizar, Arhangel and Padot na Vizantija, the latter led by Goran Trajkoski.

The company's only product, the AVE Mizar, was destroyed in a crash in 1973 which also killed Smolinski.

In conception, this is far closer to the AVE Mizar of the early 1970s than to Taylor's designs, the vehicle portions of which were purpose-designed and built.

Arhangel inherited certain features of Mizar but with a more conventional rock approach which is why Arhangel was sometimes referred as the Rock Mizar.

To the unaided eye, a more prominent star such as Sirius or Arcturus appears larger than a less prominent star such as Mizar, which in turn appears larger than a truly faint star such as Alcor.

Astronomer Sir Patrick Moore has suggested that this in fact refers to another star which lies visually between Mizar and Alcor.

The Mizar Mathematical Library is the largest coherent body of strictly formalized mathematics in existence.

Thus, a typical Mizar article is about four times as long as an equivalent paper written in ordinary style.

The full text of the MML is distributed with the Mizar checker and can be freely downloaded from the Mizar website.

It is written in Free Pascal and the source code is available to all members of the Association of Mizar Users.

* Mizar is often said to have been the first binary star discovered when it was observed in 1650 by Giovanni Battista Riccioli < sup >, p. 1 ; </ sup >, but it was probably observed earlier, by Benedetto Castelli and Galileo.

* In Ursa Major, the handle's middle star, Mizar, is noted to be a binary by Giambattista Riccioli.

To the surprise of all though, Mizar is revealed to be a robot controlled by King Jeff's jealous brother, Barry.

He is often credited with being one of the first to telescopically observe the star Mizar and note that it was a double star ; however, Castelli and Galileo observed it much earlier.

Mizar Six is home to the Tunkers, a strange religious sect who impose unusually stringent restrictions on clothing, behaviour and vocabulary, all in order to prevent needless speculation on each others ' motives.

Another difference with the original Aerocar ( and similarity to the Mizar ) is that the flight module is not designed to be taken away from the airfield.

Mizar () is a Macedonian rock band from Skopje.