Arithmetics are pointed unary systems, whose unary operation is injective successor, and with distinguished element 0.

He received his Ph. D. from CUNY in 1969 under the advisor Raymond Smullyan ; his dissertation was on " Goldbach Sentences in Some Abstract Arithmetics Constructed from a Generalization of Ordinary Recursive Arithmetic ".

His report card at the Colégio Pedro II in Rio de Janeiro records that he once failed an Algebra exam, and barely passed one on Arithmetics.

Two binary abaci constructed by Dr. Robert C. Good, Jr., made from two Chinese abaci

Two point sources will each produce an Airy pattern – see the photo of a binary star.

Two opposite ' head ' senses work as binary poles, while ' satellite ' synonyms connect to each of the heads via synonymy relations.

Two common examples are " binary phase-shift keying " ( BPSK ) which uses two phases, and " quadrature phase-shift keying " ( QPSK ) which uses four phases, although any number of phases may be used.

Two different 1953 patent applications give " Gray code " as an alternative name for the " reflected binary code "; one of those also lists " minimum error code " and " cyclic permutation code " among the names.

Ring-like structures or Ringoids: Two binary operations, often called addition and multiplication, with multiplication distributing over addition.

Lattice structures: Two or more binary operations, including operations called meet and join, connected by the absorption law.

Two of these can be resolved into their component binary systems on nights with good seeing, giving a total of six stars.

Two binary operations, say ¤ and *, are said to be connected by the absorption law if:

Two well-known examples of commutative binary operations:

Two to the power of, written as, is the number of ways the bits in a binary word of length can be arranged.

Two files that are binary compatible will have the same pattern of zeros and ones in the data portion of the file.

Two other binary values were included in an attribute ; a BRIGHT bit indicating one of two brightness levels for the two colors, and a FLASH bit, which, when set, caused the two colors to be swapped at regular intervals.

Two radio frequencies represent binary 0 and 1.

Two other stars appear close to the line of sight of Beta Lyrae, but are not part of the binary system.

Two historical anthropologists favored a binary racial classification system that divided people into a light skin and dark skin categories.

* Two binary operations, addition and multiplication, denoted by infix + and by concatenation, respectively.

Two years later, an orbital period of 1. 571 days was found by American astronomer Solon Irving Bailey, but it would not be until 1927 that the orbit of this spectroscopic binary was determined by Russian astronomer Otto Struve and American astrophysicist Christian T. Elvey.

Two privately owned radio stations began operations in 1999.

Two typical components of a CPU are the arithmetic logic unit ( ALU ), which performs arithmetic and logical operations, and the control unit ( CU ), which extracts instructions from memory and decodes and executes them, calling on the ALU when necessary.

* 1903: Two first diesel-powered ships were launched, both for river and canal operations: Petite-Pierre in France, powered by Dyckhoff-built diesels, and Vandal tanker in Russia, powered by Swedish-built diesels with an electrical transmission.

Two Deputy CGS positions include the Deputy CGS for planning, operations and readiness, under whom operates the General Staff of the ARM, and the Deputy CGS for civil-military cooperation.

Two simultaneous airborne operations were launched.

Two additional access transistors serve to control the access to a storage cell during read and write operations.

Two other Texas Air Corporation affiliates joined Eastern during the 1980s: Concourse D was also used by Braniff International Airways for Latin American operations up until their shutdown in 1982, and Continental Airlines used gates on the west side of the concourse during the 1980s.

Two civilians were killed in these operations.

Two of the SBS's four squadrons, C and X, are configured for general operations.

Two years later, at the time of The Spy Who Came in from the Cold, Mundt has risen from the field to the upper-echelon of the Abteilung, because of his successful counter-intelligence operations against the spy networks of the British Secret Service.

Two large operations were launched from this area: the St. Mihiel offensive and the Meuse-Argonne offensive, both in September.

Two of Canrobert's four divisions, supervised by General Forey, were allotted the western siege operations around the city, from the Black Sea to the Dockyard Creek ; the other two divisions, under General Bosquet, would act as a covering force along the Sapouné Heights.

Two days later, ten surplus T-28s arrived from South Vietnam ; four were retained by Waterpump so it could resume training operations while the other six were passed on to the RLAF.

Two spaces X and Y are homotopy equivalent if they can be transformed into one another by bending, shrinking and expanding operations.

Two other aeromedical transport squadrons followed that year, primarily because of the impracticality of converting their locations to modern jet fighter operations.

* Two XOR operations suffice to do the traversal from one item to the next, the same instructions sufficing in both cases.

Two engineers drive the train and handle related operations.

Two days later, the British prime minister, Winston Churchill sent a memo to his chief staff officer, General Hastings Ismay, asking him to begin planning an operation for a raid on the islands as soon as possible and stating that he felt that it would be the type of operations that the newly formed Commandos would be suited for.

* Two army officers who lead retaliation expeditions against Indians for winter raiding parties on settlers used the term, one to describe operations in Ohio and Indiana in 1790, the other in Pennsylvania in 1794.

Two very useful ways for modifying a form-dictionary are the addition to the dictionary of complete paradigms rather than single forms and the application of a single change to more than one dictionary form.

Two positive results in addition to the discharge itself are enough to diagnose BV.

In addition, seven pretenders represent exiled dynastic monarchies in Brazil, France, Spain, Portugal, Parma and Two Sicilies.

Two ’ s complement arithmetic is convenient because there is a perfect one-to-one correspondence between representations and values ( in particular, no separate + 0 and − 0 ), and because addition, subtraction and multiplication do not need to distinguish between signed and unsigned types.

The Mole Trilogy is made up of parts I, II ( The Tunes of Two Cities ) and IV ( The Big Bubble: Part Four of The Mole Trilogy ), in addition to releases of related material such as Intermission.

Among the works exhibited were Le Fauconnier's vast composition Les Montagnards attaqués par des ours ( Mountaineers Attacked by Bears ) now at Rhode Island School of Design Museum, Joseph Csaky's Deux Femme, Two Women ( a sculpture now lost ), in addition to the highly abstract paintings by Kupka, Amorpha ( The National Gallery, Prague ), and Picabia, La Source, The Spring ( Museum of Modern Art, New York ).

Two chariot racing factions, the Blues and the Greens, were involved in the Nika riots which lasted around a week in 532 CE ; nearly half the city was burned or destroyed in addition to tens of thousands of deaths.

In addition to more manufacturers, Phase Two plans include adding to the sport's international appeal by including races in India, Korea, Hong Kong, Singapore and South Africa, as well as two brand-new domestic races.

In addition to the Phase Two plans, the FIA has announced that V8 Supercars will head to the Circuit of the Americas in Austin, Texas in 2013.

In addition, she won a Golden Globe Award for Best Supporting Actress in a Series, Mini-series, or Motion Picture Made for Television for her role in The Two Mrs. Grenvilles ( 1988 ), and was nominated for an Emmy Award for the same.

American educator Seymour Eaton wrote the children's book series The Roosevelt Bears, while composer John Bratton wrote " The Teddy Bear Two Step " which, with the addition of Jimmy Kennedy's lyrics, became the song " The Teddy Bears ' Picnic ".

Two player demands were satisfied with the addition of Trammel: a rule set that does not allow non-consensual PVP, and additional open land for player housing.

All Adopt-A-Dino donors will be recognized in the following season's ROAR Magazine, in addition to receiving: Two all-sport season passes valid for all Dinos regular season home games, a plaque-mounted photo of your chosen athlete or team, an invitation to a free event to meet an interact with your chosen team, and a tax receipt for $ 890.

After the addition of the railroad in 1888, the mines began shipping the iron ore to the docks of Lake Superior in Two Harbors.

In addition to Two Guys there was a Woolworth, Montgomery Wards, several grocery stores, and various other shops along Broadway.

In a paper published in 1894, Traube proposed the addition of chloride of lime ( calcium hypochlorite ) to water to render it “ germ-free .” Two other investigators confirmed Traube ’ s findings and published their papers in 1895.

In addition to this, in 1988 the New Zealand Government issued reparations for those who were prisoners of war in Germany during World War Two and not those in Japan, which Drake alleged was discrimination.

Two yomihon masterpieces were written by Ueda Akinari: Ugetsu monogatari and Harusame monogatari wrote the extremely popular fantasy / historical romance Nansō Satomi Hakkenden in addition to other yomihon.

In addition to Equus, he also appeared in Broadway productions of A Memory of Two Mondays and A Few Good Men, for which he was a Tony Award nominee in 1990.

Two years afterwards, on the recommendation of Gronovius, he was chosen to succeed that scholar at Deventer ; in 1662 he moved to the University of Utrecht, where he occupied first the chair of rhetoric, and in addition, from 1667 until his death, that of history and politics.

Two former students of Trungpa, John Steinbeck IV and his wife, wrote a sharply critical memoir of their lives with him in which they claim that, in addition to alcohol, Trungpa used $ 40, 000 a year worth of cocaine, and used Seconal to come down from the cocaine.

Telescreens, in addition to being surveillance devices, are also the equivalent of televisions ( hence the name ), regularly broadcasting false news reports about Oceania's military victories, economic production figures, spirited renditions of the national anthem to heighten patriotism, and Two Minutes Hate, which is a two-minute film of Emmanuel Goldstein's wishes for freedom of speech and press, which the citizens have been trained to disagree with.