All these contributions involve proofs that the models are computationally equivalent to the Turing machine ; such models are said to be Turing complete.

All of these early attempts made at trying to formulate non-Euclidean geometry however provided flawed proofs of the parallel postulate, containing assumptions that were essentially equivalent to the parallel postulate.

All of the above proofs use the axiom of choice ( AC ) in some way.

All proofs below use the notion of the adjugate matrix of an n × n matrix M. This is a matrix whose coefficients are given by polynomial expressions in the coefficients of M ( in fact by certain ( n − 1 )×( n − 1 ) determinants ), in such a way that one has the following fundamental relations

Near the end of a review of the doctrine's history – a review which serves as the bulk of Munificentissimus Deus – Pope Pius XII tells us: " All these proofs and considerations of the holy Fathers and the theologians are based upon the Sacred Writings as their ultimate foundation.

All known proofs of that theorem make use of characters.

All the specimens of which it is composed, are in the highest and most exquisite state of preservation, such an extensive collection can be supposed to be, and a very considerable number are unique, such as are not to be found in any other Cabinet whatever, and of considerable value ; many of which, coming from countries exceedingly unhealthy, where the collectors, in procuring them, have perished by the severity of the climate, give but little room to expect any duplicate will ever be obtained during the present age ; and the learned quotations that have been taken from it by those celebrated authors Linnaeus and Fabricius, in all their late editions, are incontestable proofs of the high degrees of estimation they entertained of it.

All entries in the ASCII table below code 32 ( technically the C0 control code set ) and 127 are of this kind, including BEL ( which is intended to cause an audible signal in the receiving terminal ), SYN ( which is a synchronization signal ), and ENQ ( a signal that is intended to trigger a response at the receiving end, to see if it is still present ).

All Italian-Canadians were denied RAI programming by RAI International's removal of its programming from the Canadian marketplace, a move intended to create a public outcry and a threat that Canadians would resort to using satellite viewing cards obtained via the US in order to watch RAI, even though these cards were either grey market or black market, according to different analyses ( see below ).

All current formats, which are listed below, are PCM based.

All of the FFT algorithms discussed below compute the DFT exactly ( in exact arithmetic, i. e. neglecting floating-point errors ).

All signage on highways and roads in Hong Kong are bilingual ( traditional Chinese below and English above ).

In 1975, the All Japan Kendo Federation ( AJKF ) developed then published " The Concept and Purpose of Kendo " which is reproduced below.

Listed below are the 28 categories tabulated in the 2000 United States Census: Mexican, Puerto Rican, Cuban, Dominican Republic ; Central American: Costa Rican, Guatemalan, Honduran, Nicaraguan, Panamanian, Salvadoran, Other Central American ; South American: Argentinian, Bolivian, Chilean, Colombian, Ecuadorian, Paraguayan, Peruvian, Uruguayan, Venezuelan, Other South American ; Other Hispanic or Latino: Spaniard, Spanish, Spanish American, All other Hispanic or Latino.

All coins below 1 markka had ceased to be produced by 1948.

All methods depend upon an implicit or explicit mathematical model describing the evolution of characters observed in the species included ; all can be, and are, used for molecular data, wherein the characters are aligned nucleotide or amino acid sequences, and all but maximum likelihood ( see below ) can be, and are, used for morphological data.

It has all come about in a few months .... All stairways lead to the roof, where residents are arranging to rig up a loudspeaker, connected with instruments below.

All the instruments were given an initial written range from the B below the treble staff to the F, one space above the three ledger lines above staff, giving each saxophone a range of two and a half octaves.

Another 30 artificial radioisotopes of tungsten have been characterized, the most stable of which are < sup > 181 </ sup > W with a half-life of 121. 2 days, < sup > 185 </ sup > W with a half-life of 75. 1 days, < sup > 188 </ sup > W with a half-life of 69. 4 days, < sup > 178 </ sup > W with a half-life of 21. 6 days, and < sup > 187 </ sup > W with a half-life of 23. 72 h. All of the remaining radioactive isotopes have half-lives of less than 3 hours, and most of these have half-lives below 8 minutes.

All of the remaining radioactive isotopes have half-lives shorter than an hour, most of which are below 10 seconds.

All materials, solid or liquid, have a small vapour pressure, and their outgassing becomes important when the vacuum pressure falls below this vapour pressure.

Titanic causes the deaths of nearly 1, 500 people and attracts global and historical attention ; Title bar: All the events below are part of World War I ; French Army lookout at his observation post in 1917 ; Russian troops awaiting a German attack ; A ration party of the Royal Irish Rifles in a communication trench during the Battle of the Somme ; Vladimir Lenin addresses a crowd in the midst of the October Revolution of 1917 ; A flu pandemic in 1918 kills tens of millions worldwide .| 420px | thumb

All vertebrates are built along the basic chordate body plan: a stiff rod running through the length of the animal ( vertebral column or notochord ), with a hollow tube of nervous tissue ( the spinal cord ) above it and the gastrointestinal tract below.

All possible transitions can be shown as below:

All but the earliest versions of X. 25 include facilities which provide for OSI network layer Addressing ( NSAP addressing, see below ).

All refugees in the world are under the UNHCR mandate except Palestinian Arabs, who fled the future Jewish state between 1947 and 1949 ( see below ), and their descendants.

All overnight camping below the rim requires a backcountry permit from the Backcountry Office ( BCO ).

All known black hole candidates are so large that their temperature is far below that of the cosmic background radiation, so they are all gaining energy.

All in all, in cultures that practice sex-selective abortion, women are prone to sexual discrimination and are viewed below status to men.

All economic sectors ranging from manufacturing and agriculture to tourism and finance, declined sharply after independence from Portugal in 1975, but picked up in the 2000s after the end of the Mozambican Civil War, although they are still performing well below potential.

All display modes that use a pixel clock below 165 MHz, and have at most 24 bits per pixel, are required to use single-link mode.

All of these sub-tests involve reading except Arithmetic Computation.

All these games involve players drawing and discarding tiles or cards to make melds.

All navigational techniques involve locating the navigator's position compared to known locations or patterns.

All professions involve technical, specialised and highly skilled work often referred to as " professional expertise.

All forms of albinism involve abnormal production and / or deposition of melanin.

All transit services, except personal rapid transit, involve a trade-off between speed and frequency of stops.

All sores involve a breakdown in the walls of the fine membrane of the vaginal wall.

All of these approaches involve a historical and sociological turn to science, with a special emphasis on lived experience ( a kind of Husserlian " life-world "), rather than a progress-based or anti-historical approach as done in the analytic tradition.

All of the tenants ' names involve a pun on the character's room number:

# All elections must involve a direct, equal, secret, and universal vote

All examples in this section involve associative operators, thus we shall use the terms left / right inverse for the unital magma-based definition, and quasi-inverse for its more general version.

All Formula One events and MotoGP events with Sunday races involve qualifying taking place on Saturday.

All the main political groups involve children in this way, including Fatah, Hamas, Islamic Jihad, and the Popular Front for the Liberation of Palestine.

All involve lawmen working against an entrenched criminal element, partially by " holing up " in their jailhouse.

All deal with distance, time and force but strategy is large scale, can endure through years, and is societal while tactics are small scale and involve the disposition of fewer elements enduring hours to weeks.

All of the scenes that take place outside of the 24-month period of the primary story involve flashbacks from Mickey's previous marriage to Hannah, Hannah and Mickey's struggle with infertility, his subsequent role as a surrogate father to Hannah's children, and his first date with Hannah's sister Holly ( Dianne Wiest ).

All procedures for picking a passphrase involve a tradeoff between security and ease of use ; security should be at least " adequate " while not " too seriously " annoying users.

All atomic reactions involve changing one atom into another by changing the nucleus.

All AHF-supported projects involve community participation, in order to build local capacity and to ensure the foundation is responding to community needs.

All incarnations of the Ghost in the Shell franchise deeply involve Theseus ' Paradox in terms of full-body prosthetics.

All meanings involve a situation in which a person is working, unlike unemployment, where a person who is searching for work cannot find a job.

All meanings involve under-utilization of labor which is missed by most official ( governmental agency ) definitions and measurements of unemployment.

All his cooking endeavors seem to involve him actually cooking himself, somehow transforming his actual body into whatever it was he was supposed to be cooking ( such as covering himself in dough, dipping his head into a vat of lard, and emerging with his head as a perfect, chocolate frosted doughnut ).