Identities are equations formulated using only the operations the structure allows, and variables that are tacitly universally quantified over the relevant universe.

These exams are proctored by Mensa and do not provide a quantified score ; they serve only to qualify a person for membership.

Seen in this way, the demand that policy rely only on what is proven to be " scientific truth " would be a prescription for policy paralysis and amount in practice to advocacy of acceptance of all of the quantified and unquantified costs and risks associated with policy inaction.

NBG's principle of class comprehension is predicative ; quantified variables in the defining formula can range only over sets.

The boolean satisfiability problem can be viewed as the special case where all variables are existentially quantified, allowing ordinary nondeterminism, which uses only existential branching, to solve it efficiently.

The computational hardness assumption is that bridging this gap can only to be done by lengthy calculation, when quantified in terms of the size of N.

Huey studied and quantified regressions ( only a small proportion of saccades are regressions ), and he showed that some words in a sentence are not fixated.

Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored.

More consequentially, the quantified variables in φ ( x ) may range over all classes and not just over all sets ; this is the only way MK differs from NBG.

Note that p and s in Power Set and Union are universally, not existentially, quantified, as Class Comprehension suffices to establish the existence of p and s. Power Set and Union only serve to establish that p and s cannot be proper classes.

It is the gait of the human who must run to live: arms dangling, legs barely swinging over the ground, head hung down and only occasionally swinging up to see the target, a loose motion that is just short of stumbling and yet is wonderfully graceful.

In some armies only designated artillery HQs have the tactical fire control authority to order fire units to engage a target, all ' calls for fire ' being requests to these HQs.

Also, using microbial methods, bacteria can be suitably modified to be effective in only a narrow environmental range, the range of the target that distinctly differs from the army on the offensive.

Thus only the target might be affected adversely.

Due to the large number of calculations, a work in progress is usually only rendered in detail appropriate to the portion of the work being developed at a given time, so in the initial stages of modeling, wireframe and ray casting may be used, even where the target output is ray tracing with radiosity.

Their groups ( C, CC, CXC, CX < sub > 3 </ sub > C chemokines ) represent not only structurally related molecules with a special arrangement of disulfide bridges, but their target cell specificity is also diverse: CC chemokines act on monocytes ( e. g. RANTES ), CXC chemokines are neutrophil granulocyte specific ( e. g. IL-8 ).

Data compression can be viewed as a special case of data differencing: Data differencing consists of producing a difference given a source and a target, with patching producing a target given a source and a difference, while data compression consists of producing a compressed file given a target, and decompression consists of producing a target given only a compressed file.

In the 30s and 40s, it was widely accepted that genes were the target of selection, because that was the only way they could be made accessible to mathematics, but now we know that it is really the whole genotype of the individual, not the gene.

Bombed as a target of the Oil Campaign of World War II, Erfurt suffered only limited damage and was captured on 12 April 1945, by the US 80th Infantry Division.

It is worn only in foil and sabre, and serves to distinguish hits on target from those that are off-target.

The peace would only last until the Ottoman Empire had declined enough to become a target for the others.

If the target is a hard and heavy object, or if it is resting on some sort of anvil, the head can travel only a very short distance d before stopping.

When South Africa reached 248 / 8, Cronje declared ; both teams then forfeited an innings leaving England a target of 249 to win the Test, which they did with two wickets left and only five balls remaining.

The only difference between some early pitch-pipes and harmonicas is the name of the instrument, which reflected the maker's target audience.

Major won by 218 votes to Redwood's 89 ( with 12 spoiled ballots, eight ' active ' abstentions and two MPs abstaining ), enough to win in the first round, but only three more than the target he had privately set himself.

The night-time raids were intended to target only military sites on the east coast and around the Thames estuary, but after blackouts became widespread, many bombs fell randomly in East Anglia.

Remarkable is that this target consisted of only 10 < sup > 9 </ sup > atoms of highly radioactive < sup > 253 </ sup > Es ( with a half-life of 20. 5 days ).

German social scientists Gunnar Heinsohn and Otto Steiger theorize that midwifery became a target of persecution and repression by public authorities because midwives not only possessed highly specialized knowledge and skills regarding assisting birth, but also regarding contraception and abortion.

Microcontrollers were originally programmed only in assembly language, but various high-level programming languages are now also in common use to target microcontrollers.

Many neurons have only one axon, but this axon may — and usually will — undergo extensive branching, enabling communication with many target cells.

Because it is a biological scavenger ( and universal target ) it is currently the only therapeutic agent effective in providing complete stoichiometric protection against the entire spectrum of organo-phosphorus nerve agents.

This supported only the VAR data type, which was an integral type corresponding to the native word length of the target architecture, and arrays of only one dimension.

The only factors that are personally set by the choreographer are the movements themselves, the number of the dancers, and the approximate total duration of the dance.

Not only did constellations like Draco, Cepheus, and Cassiopeia spin circles around the pole, but stars which were not circumpolar rose and set at the same place on the horizon each night.

For by now the original cause of the quarrel, Philip's seizure of Gascony, was only one strand in the spider web of French interests that overlay all western Europe and that had been so well and closely spun that the lightest movement could set it trembling from one end to the other.

The first substantially complete stereo Giselle ( and the only one of its scope since Feyer's four-sided LP edition of 1958 for Angel ), this set is, I'm afraid, likely to provide more horrid fascination than enjoyment.

After the frames and transom are set up on the jig and temporarily braced, a piece of three-inch-wide mahogany ( only widths will be given since the 13/16-inch thickness is used throughout ) is butted between frames one and two below the line of the keelson.

You then descended one story, glommed a television set from the music room -- the only constructive feature of your visit, by the way -- and, returning to the ground floor, entered the master bedroom.

These areas, by virtue of their abrupt density of pattern, stated the literal surface with such new and superior force that the resulting contrast drove the simulated printing into a depth from which it could be rescued -- and set to shuttling again -- only by conventional perspective ; ;

For the only time in the opera, words are not set according to their natural inflection ; ;

In Pimen's cell the soft prayers of the monks, heard from offstage, not only help to set the scene but emphasize the contrast between young Grigori's thoughts and his situation.

Members of the young set who would like to come to the party only during the dancing time are welcomed.

It seems like only last year that we watched them set out up the hill hand in hand on a rainy day in their yellow raincoats to finger-paint at the grammar school.

The statement also points to a classic paradox: The more men turn toward God, who is not only in himself the paradigm of all unity but also the only ground on which human unity can ultimately be established, the more men splinter into groups and set themselves apart from one another.

Now to him who is able to preserve you without sin and to set you before the presence of his glory, without blemish, in gladness, to the only God our Savior, through Jesus Christ our Lord, belong glory and majesty, dominion and authority, before all time, and now, and forever.

The Jazz Three displayed their sound musicianship, not only in their own chosen set, but as the emergency accompanists for Al Minns & Leon James, the superb jazz dancers who have now been Newport performers for three successive years, gradually moving up from a morning seminar on the evolution of the blues to a spot on the evening program.

But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.

Research in the field of microbiomes shows that only a limited set of microbes cause tooth decay, with most of the bacteria in the human mouth being harmless.

Its domain is the powerset of A ( with the empty set removed ), and so makes sense for any set A, whereas with the definition used elsewhere in this article, the domain of a choice function on a collection of sets is that collection, and so only makes sense for sets of sets.

For example, after having established that the set X contains only non-empty sets, a mathematician might have said " let F ( s ) be one of the members of s for all s in X.

" The problem then becomes that of constructing a well-ordering, which turns out to require the axiom of choice for its existence ; every set can be well-ordered if and only if the axiom of choice holds.

For example, if we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬ AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets.

Provided that an applet is hosted by an operating system, it can function as any other normal software application but is and performs only a small set of tasks.

It was intended to be a flexible set of laws that could only be strengthened, not weakened, by future case law.