* 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 Mizar system consists of a formal language for writing mathematical definitions and proofs, a proof assistant which is able to mechanically check proofs written in this language, and a library of formalized mathematics which can be used in the proof of new theorems.

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 – 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.

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.

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.

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.

This and other fears of the solar system have disappeared gradually, first, with the Ptolemaic system and its built-in concept of periodicity and then, more firmly, with the Newtonian innovation of an universal force that could account quantitatively for both terrestial and celestial motions.

In spite of the dreams of the host for oneness in the group, the Af incoming messages for each guest overload his receiving system beyond comprehension if N exceeds about six.

In any social system in which communications have an importance comparable with that of production and other human factors, a point like f in Figure 2 would ( other things being equal ) be the dwelling place for the community leader, while e and h would house the next most important citizens.

The problem is rather to find out what is actually happening, and this is especially difficult for the reason that `` we are busily being defended from a knowledge of the present, sometimes by the very agencies -- our educational system, our mass media, our statesmen -- on which we have had to rely most heavily for understanding of ourselves ''.

This is necessary for a sounder collective defense system.

It is possible that international organization will ultimately supplant the multi-state system, but its proper function for the immediate future is to reform and supplement that system in order to render pluralism more compatible with an interdependent world.

Does the organization show an affinity for a foreign government, political party or personality in opposition or preference to the American system??

And just how far can the Legislature go toward setting up a self-insurance system for the state in the midst of a governor's race ''??

The education program for retarded children conducted by the East Greenwich school system has pupils from at least one neighboring community.

The arguments advanced by those individuals and groups who oppose the system in force and who would drastically curtail or do away entirely with hospital care for the non-service-connected case, seem to be coldly impractical and out-of-step with the wishes of the general public.

An adequate system of VA hospitals is better equipped to care for the veterans than any 50 state hospitals.

The highway system is an agency of government, and when it grinds up 40,000 Americans every year the government is destroying its own taxpayers, which is obviously a silly thing for any government to do.

Was it the party's intention, for example, to abolish gradually the kolkhoz system and replace it by uniformly wage-earning kolkhozes, i.e., state farms ( which were, moreover, to be progressively `` urbanized '' )??

Behind were privies, for there was no sewage system.

The Farm Credit Administration, an independent agency located within the Department of Agriculture, supervises and coordinates a cooperative credit system for agriculture.

The system is composed of three credit services, Federal Land Banks and National Farm Loan Associations, Federal Intermediate ( short-term ) Credit Banks, and Banks for Cooperatives.

The credit provdied by the first two services in the system outlined above is primarily for general agricultural purposes.

This condition will undoubtedly continue until such time as a state uniform system of evaluation is established, or through mutual agreement of the local assessing officials for a method of standard assessment practice to be adopted.

There we held `` that the statutory scheme for review, within the selective service system, entitles [ conscientious objectors ] to no guarantee that the FBI reports must be produced for their inspection ''.

Because administration of the forest highway system is a responsibility of the Secretary of Commerce with maintenance provided by the States and counties, this Development Program for the National Forests does not include estimates of the funds needed to maintain the forest highway system nor to construct the additions to it that are needed.