In class theories such as Von Neumann – Bernays – Gödel set theory and Morse – Kelley set theory, there is a possible axiom called the axiom of global choice which is stronger than the axiom of choice for sets because it also applies to proper classes.

Basic theories, such as arithmetic, real analysis and complex analysis are often introduced non-axiomatically, but implicitly or explicitly there is generally an assumption that the axioms being used are the axioms of Zermelo – Fraenkel set theory with choice, abbreviated ZFC, or some very similar system of axiomatic set theory like Von Neumann – Bernays – Gödel set theory, a conservative extension of ZFC.

Von Neumann wrote the first array-sorting program ( merge sort ) in 1945, during the building of the first stored-program computer .< sup > p.

Pfanzagl's axiomatization was endorsed by Oskar Morgenstern: " Von Neumann and I have anticipated " the question whether probabilities " might, perhaps more typically, be subjective and have stated specifically that in the latter case axioms could be found from which could derive the desired numerical utility together with a number for the probabilities ( cf.

Von Neumann machines differ in having a memory in which they store their operating instructions and data.

The modern computer, or Von Neumann machine, would play a central role in cognitive science, both as a metaphor for the mind, and as a tool for investigation.

Some argue that the concept of the collapse of a " real " wave function was introduced by Heisenberg and later developed by John Von Neumann in 1932.

Von Neumann himself used the term Universal Constructor.

As a serious proposal, it was first suggested by mathematician John Von Neumann in the late 1940s when he proposed a kinematic self-reproducing automaton model as a thought experiment.

See Von Neumann, J., 1966, The Theory of Self-reproducing Automata, A. Burks, ed., Univ.

The design could be modified to build Von Neumann probes to explore the galaxy.

The movie Screamers, based on Dick's short story Second Variety, features a group of robot weapons created by mankind to act as Von Neumann devices / berserkers.

In 1968, just before he published the first volume, Knuth accepted a job working on problems for the National Security Agency ( NSA ) through their FFRDC the Institute for Defense Analyses ( IDA ) Communications Research Division situated at the time on the Princeton campus in the Von Neumann building as stated in his cumulae vitae.

In work on Zermelo – Fraenkel set theory, the notion of class is informal, whereas other set theories, such as Von Neumann – Bernays – Gödel set theory, axiomatize the notion of " class ", e. g., as entities that are not members of another entity.

In September 2011 researchers also proved that a quantum computer can be made with a Von Neumann architecture ( separation of RAM ).

* Von Neumann machine

* Mathematics: Von Neumann universe

As far as computer security is concerned, reasoning about the security properties of a computer system requires being able to make sound assumptions about what it can, and more importantly, cannot do ; however, barring any reason to believe otherwise, a computer is able to do everything that a general Von Neumann machine can.

Von Neumann machine may refer to:.

* Von Neumann architecture, a conceptual model of a computer architecture

** Von Neumann probes, hypothetical space probes capable of self-replication

Von Neumann used 10 digit numbers, but the process was the same.

Von Neumann was aware of this, but he found the approach sufficient for his purposes, and was worried that mathematical " fixes " would simply hide errors rather than remove them.

Von Neumann judged hardware random number generators unsuitable, for, if they did not record the output generated, they could not later be tested for errors.

Both Von Neumann as well as various degrees of Harvard architectures are used.

Von Trier has stated he was inspired to make a trilogy about the United States as a reaction to Americans at the Cannes film festival who said he had no right to make the Dancer in the Dark, which was often viewed as being critical of a country he has never been to ( and has no intention of ever visiting, due to his phobia of travel ); however, von Trier himself has stated in interviews he did not intend it to be a criticism of America, saying the film takes place in a " fictional America ".

Indeed Von Braun said of him:

Von Mueller's early records also mention two trees on the nearby Black Spur Range, one alive and measuring and another fallen tree said to measure, but these were either based on hearsay or uncertain reliability.

Von Daniken said that the lines were built following instructions from extraterrestrial beings, to be used as airfields for their spaceships.

Speaking in a 2001 documentary, Von Däniken said that although he could not conclusively prove to the scientific community that any of the items in his archive were of alien origin, he felt that " today's science " would not accept such evidence, as " the time is simply not right ".

After the New York State Supreme Court authorized the state to force feed him, Dr. Martin Von Holden, the director of the Central New York Psychiatric Center, said Chapman still refused to eat with other inmates but agreed to take liquid nutrients.

Said Plummer of the film and his role in a December 2009 interview, " I was a bit bored with the character ( of Captain Von Trapp )", said Plummer.

Von Braun said he was thoroughly convinced the aircraft would be able to transport the largest of NASA's cargo.

Hitler reportedly said of him, " Nobody in the world but Von Bock can teach soldiers to die.

It was also at this point that Kerry Von Erich was involved in a motorcycle accident ( June 4, 1986 ) and suffered injuries that later worsened when he attempted to return to the ring too soon ( an attempt said by some observers to have taken place under heavy pressure from Fritz ) and would finally necessitate the amputation of his right foot.

The Constitutions of the Holy Apostles Book II. 24 refers to the passage “ And when the elders had set another woman who had sinned before Him, and had left the sentence to Him, and were gone out, our Lord, the Searcher of the hearts, inquiring of her whether the elders had condemned her, and being answered No, He said unto her: “ Go thy way therefore, for neither do I condemn thee .” Book II is generally dated to the late third century ( Von Drey, Krabbe, Bunsen, Funk ).

* In science-fiction stories Samolot von Ribbentrop ( Von Ribbentrop's plane ) and Atomowa Ruletka ( Nuclear Roulette ) by Polish writer Andrzej Pilipiuk, " red mercury reactors " are used as highly efficient power sources, although no further information about either the substance or said reactors is given.

Von Lettow-Vorbeck's fluency in the Swahili language earned the respect and admiration of his African soldiers ; he appointed black officers and " said — and believed — ' we are all Africans here '.

Von Erck said he got the idea for the website while watching people attempt to groom young girls in chat rooms in Oregon.

Don McGlashan said of Von Sturmer, " Richard was a really prolific writer-and still is.

) According to reports, His Majesty the King has telegraphed Captain Von Jachmann expressing the very highest recognition for the courage on the part of the navy in the face of great enemy superiority and to deigning to promote the said officer to rank of rear admiral.

" Von Rhein praised the group in 2007 as " singing with the pure tone, clear vowels and firm blend of an English cathedral choir " and said that " melodic leaps, intricately laced part-writing and other musical hurdles were met most handsomely by the 23-member chorus.

Von Knyphausen returned to Europe, having, as he said, achieved neither glory nor advancement.

A week later on February 6, 1984 in Ft. Worth, in what would turn out to be his last interview, David Von Erich expressed his happiness over Mike lasting 10 minutes with Ric Flair and said that now he ( David ) would get to name every single stipulation in David's return match with Flair.

Belasyse in particular was said to have been designated Commander-in-Chief of the Popish army, but Charles II, according to Von Ranke, ridiculed the idea on the ground that the man could then hardly stand on his feet with gout.

On the DVD " The Triumphs and Tragedies of World Class Championship Wrestling ," Kevin Von Erich said that he, as well as most of the family, was adamantly against bringing Vaughan in as another Von Erich, but Fritz was adamant, especially as Kevin and Kerry were wrestling two or three times a day in various places throughout the Texas territory.

When demands for more money in 1987 were not met by Fritz, Vaughan jumped to WCCW's territorial rival Wild West Wrestling without giving notice, and in a rare breach of kayfabe, Vaughan's non-relationship to the family was exposed by Fritz on television in retaliation, saying that Vaughan was " in no way, shape or form related to the Von Erich family " and Fritz said he never planned on mentioning Vaughan's name again.

According to Manning, he said that Hernandez had three times the amount of cocaine in his system that would have resulted in a fatality, and he and Kevin Von Erich stated that Gino also had cocaine in his stomach.