For extreme settings of the parameters, the definition of probabilistically checkable proofs is easily seen to be equivalent to standard complexity classes.

NOW accounts are considered checkable deposits, and are counted in the Fed's M1 definition of the money supply, as well as in the broader definitions.

Chaitin prefaces his definition with: " I'll show you can't prove that a program is ' elegant '"— such a proof would solve the Halting problem ( ibid ).

The basic idea of his proof is that a proposition that holds of x if x = n for some natural number n can be called a definition for n, and that the set

One proof of the chain rule begins with the definition of the derivative:

Noting another proof that self-replicating machines are possible is the simple fact that all living organisms are self replicating by definition.

While it is one of the most commonly used concepts in logic it must not be mistaken for a logical law ; rather, it is one of the accepted mechanisms for the construction of deductive proofs that includes the " rule of definition " and the " rule of substitution " Modus ponens allows one to eliminate a conditional statement from a logical proof or argument ( the antecedents ) and thereby not carry these antecedents forward in an ever-lengthening string of symbols ; for this reason modus ponens is sometimes called the rule of detachment.

The definition of theorems as elements of a formal language allows for results in proof theory that study the structure of formal proofs and the structure of provable formulas.

A definition is also accepted without proof since it simply gives the meaning of a word or phrase in terms of known concepts.

* A corollary is a proposition that follows with little or no proof from one other theorem or definition.

Nearly every aspect of SRA was controversial, including its definition, the source of the allegations and proof thereof, testimonials of alleged victims, and court cases involving the allegations and criminal investigations.

This allows the definition of a formal proof to be precisely specified without any ambiguity.

This proof uses definition of even integers, as well as distribution law.

: The only thing that was used in the proof that was not a definition was the sine law.

Early laws simply prohibited driving while intoxicated, requiring proof of a state of intoxication with no specific definition of what level of inebriation qualified.

A formal proof, from the definition of a derivative, is:

The international protection of refugees hardly existed before the First World War and people faced difficulty in providing proof of identity identity but also there was no internationally agreed definition of " refugee ".

The * points to Exercise # 24 ( p. 189 ) wherein he asks for a proof of the following: " In section 53, the definition of the number ' 0 ' was stated by way of an example.

The noun triviality usually refers to a simple technical aspect of some proof or definition.

Probabilistic computation is also critical for the definition of most classes of interactive proof systems, in which the verifier machine depends on randomness to avoid being predicted and tricked by the all-powerful prover machine.

For a detailed definition of free current and bound current, and the proof that the two formulations are equivalent, see the " proof " section below.

A rigorous proof of the product rule can be given using the properties of limits and the definition of the derivative as a limit of Newton's difference quotient.

On the other hand, the simplicity of the algebra in this proof perhaps makes it easier to understand than a proof using the definition of differentiation directly.

IntuiSense's patented technology includes a high definition monitor ( 55 "- 32 "), a custom built CPU, MDB monitor, and the IS Gesture Recognition system all in a vandal proof construction.

( Without an accepted definition of large cardinal property, it is not subject to proof in the ordinary sense ).

The poet was by definition a realist, his imaginings and parables being natural organizations of reality.

but this grinning, broken head, not ten feet away from me, was the sharp definition of what my reality had become.

No matter how devoted a man was, no matter how fully he gave his life to the Lord, he could never extinguish that one spark of pride that gave him definition as an individual.

It might be contended, of course, that Eichmann in stubbornly denying anti-Semitic feelings was lying or insisting on a private definition of anti-Semitism.

When her brother Winslow became a student at Brown University in 1874, she wrote him about a course in history he was taking under Professor Diman: `` What is Prof. Diman's definition of civilization, and take the world through, is its progress ever onward, or does it retrograde at times??

The 1976 definition of the astronomical unit was incomplete, in particular because it does not specify the frame of reference in which time is to be measured, but proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity was proposed, and " vigorous debate " ensued until in August 2012 the International Astronomical Union adopted the current definition of 1 astronomical unit = 149597870700 meters.

This definition was adopted by the United Nations Sub-Commission on the Promotion and Protection of Human Rights in The Despouy Report on Human Rights and Extreme Poverty.

Throughout European history, philosophers such as Aristotle and Thomas Aquinas, among others, contemplated the possibility that souls exist in animals, plants, and people ; however, the currently accepted definition of animism was only developed in the 19th century by Sir Edward Tylor, who created it as " one of anthropology's earliest concepts, if not the first ".

Edward Burnett Tylor | Sir Edward Tylor was responsible for forming the definition of animism currently accepted in anthropology.

This slump was permanent due to the introduction of a stricter definition of citizen described below.

The cubists, dadaists, Stravinsky, and many later art movements struggled against this conception that beauty was central to the definition of art, with such success that, according to Danto, " Beauty had disappeared not only from the advanced art of the 1960 ’ s but from the advanced philosophy of art of that decade as well.

Prior to this definition, it was used by Persian-speakers ( and others influenced by Persian ) to denote the Pashtun people.

Celsius was the first to perform and publish careful experiments aiming at the definition of an international temperature scale on scientific grounds.

The Lavoisier definition was held as absolute truth for over 30 years, until the 1810 article and subsequent lectures by Sir Humphry Davy in which he proved the lack of oxygen in H < sub > 2 </ sub > S, H < sub > 2 </ sub > Te, and the hydrohalic acids.

This definition was proposed by Justus von Liebig circa 1838, based on his extensive works on the chemical composition of organic acids.

The Arrhenius definition of acid – base reactions is a development of the hydrogen theory of acids, devised by Svante Arrhenius, which was used to provide a modern definition of acids and bases that followed from his work with Friedrich Wilhelm Ostwald in establishing the presence of ions in aqueous solution in 1884, and led to Arrhenius receiving the Nobel Prize in Chemistry in 1903 for " recognition of the extraordinary services ... rendered to the advancement of chemistry by his electrolytic theory of dissociation ".

One of these was the property, an essential universal true of the species, but not in the definition ( in modern terms, some examples would be grammatical language, a property of man, or a spectral pattern characteristic of an element, both of which are defined in other ways ).

For example, they might interpret a tomato as a vegetable — according to the English definition of tomato — even though the ideal Blissymbol of vegetable was restricted by Bliss to just vegetables growing underground.

This was the approach that Bessel used, and from this definition he derived several properties of the function.