Once the poetic arts are separated from the other forms, he lays down his famous definition of tragedy, which sets up standards and so lends direction to the remainder of the work.

But the facts about our Advisory Board and its members' duties are only one of several sets of facts about the quest for advice, both reliable and imaginative, on which to base our selections of Fellows.

In the frame are two sets of bars which interact with each other to prevent the operator from making dangerous moves.

There are various sets of exceptional lines, or lines whose images are not unique.

Often, therefore, there are a number of rules having the same effect, and commonly other sets of rules as well, having the opposite effect.

Thus, in `` The Story Of Ruth '' we have Ruth, Naomi, and Boaz and sets that are meticulously authentic.

The sets are remarkably elaborate for a road-show that doesn't pause long in any one place, and they are devised so that they shift with a minimum of interruption or obtrusiveness.

So the plot creaks, the sets are decaying, the costumes are pre-historic, the orchestra was sloppy and not very well connected with what the singers were doing.

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.

Another equivalent axiom only considers collections X that are essentially powersets of other sets:

In other words, the circle gets partitioned into a countable collection of disjoint sets, which are all pairwise congruent.

The pieces in this decomposition, constructed using the axiom of choice, are non-measurable sets.

** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.

For example, if one defines categories in terms of sets, that is, as sets of objects and morphisms ( usually called a small category ), or even locally small categories, whose hom-objects are sets, then there is no category of all sets, and so it is difficult for a category-theoretic formulation to apply to all sets.

These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.

Finally, sets of islands formed close to the coast of a continent are considered continental archipelagos when they form part of the same continental shelf so islands are just exposed continental shelf.

Whereas we say X is an H-set of Z if every cover of X with open sets of Z has a finite subfamily whose Z closure contains X.

An extreme form of divisio lists all sets whose only member is a member of the " divided " set.

In the later Legend of Atrahasis, Enlil, the king of the gods, sets out to eliminate humanity, whose noise is disturbing his rest.

Kronecker, now seen as one of the founders of the constructive viewpoint in mathematics, disliked much of Cantor's set theory because it asserted the existence of sets satisfying certain properties, without giving specific examples of sets whose members did indeed satisfy those properties.

This information can be phrased abstractly by letting O ( X ) be the category whose objects are the open subsets U of X and whose morphisms are the inclusion maps V → U of open sets U and V of X.

In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets.

During the fifth day Fiammetta, whose name means small flame, sets the theme of tales where lovers pass through disasters before having their love end in good fortune.

Many early radio sets had a third battery called the " C battery " ( unrelated to the present-day C cell ) whose positive terminal was connected to the cathode of the tubes ( or " ground " in most circuits ) and whose negative terminal supplied this bias voltage to the grids of the tubes.

The noble savage sets a king to reign over him, to whom he submits his life and limbs without a murmur or question and whose whole life is passed chin deep in a lake of blood ; but who, after killing incessantly, is in his turn killed by his relations and friends the moment a grey hair appears on his head.

Real intervals play an important role in the theory of integration, because they are the simplest sets whose " size " or " measure " or " length " is easy to define.

In 1996, Turner's company, Turner Broadcasting System ( whose Turner Entertainment division oversaw the film library ), was purchased by Time Warner who also owned Warner Bros .. Today, Warner Home Video holds the video rights to the entire Looney Tunes / Merrie Melodies animated output by virtue of Time Warner's ownership of Turner Entertainment — this is why their Looney Tunes Golden Collection DVD box sets include cartoons from both the pre-8 / 48 Turner-owned and post-7 / 48 Warner Bros. owned periods.

In measure theory, it is often useful to allow sets which have infinite measure and integrals whose value may be infinite.

where P is any unary predicate that does not mention A, to define a unique set whose members are precisely the sets satisfying the predicate.

: Given two sets, there is a set whose members are exactly the two given sets.

" Combinatoriality is a side effect of derived rows where combining different segments or sets such that the pitch-class content of the result fulfills certain criteria, usually the combination of hexachords which complete the full chromatic.

Combinatorial properties are not dependent on the order of the notes within a set, but only on the content of the set, and combinatoriality may exist among tetrachordal and trichordal sets, as well as between pairs of hexachords.

All-combinatorial sets are sets whose hexachords are capable of forming an aggregate with any of its basic transformations transposed.

It was also used by Alexander Scriabin, though from a diametrically opposed direction, created by his use of extremely slow harmonic rhythm which eventually led to his use of unordered pitch-class sets, usually hexachords ( of six pitches ) as harmony from which melody may also be created.

Most American television sets are cable-ready and have a television tuner capable of receiving older analog cable TV ( UK televisions are set up to receive Freeview digital terrestrial broadcasting ).

Importantly, as interactions between proteins are reversible, and depend heavily on the availability of different groups of partner proteins to form aggregates that are capable to carry out discrete sets of function, study of the interactions between specific proteins is a key to understand important aspects of cellular function, and ultimately the properties that distinguish particular cell types.

The government has already built 155 sets of wind turbines capable of producing 281. 6 MW of energy, and additional projects are planned or under construction.

To look at the universe of all sets not as a fixed entity but as an entity capable of " growing ", i. e., we are able to " produce " bigger and bigger sets.

This had four sets of gates, so that it could be used at all states of the tide, was capable of holding vessels which were, and used a system of sluices to enable the channel through Lake Lothing to be flushed with water from Oulton Broad.

Such oscillation sets up a low-frequency atmospheric gravity wave capable of affecting both atmospheric and oceanic currents in the region.

Diamond was to be a new, integrated product line capable of sharing large sets of data across applications.

; Real time question answering: There is need for developing Q & A systems that are capable of extracting answers from large data sets in several seconds, regardless of the complexity of the question, the size and multitude of the data sources or the ambiguity of the question.

* Because of these differences, some Australian TV sets ( when taken to NZ ) are only be capable of mono sound reproduction, and many VHF channels may not be received ( properly ) or come in at all.

In principle, this could lead to the development of complex catalytic sets capable of self-maintenance.

However, interlaced signal requires a display that is natively capable to show the individual fields in a sequential order, and only traditional CRT-based TV sets are capable of displaying interlaced signal, due to the electronic scanning and lack of apparent fixed resolution.

Many area households probably did not have sets capable of receiving the station's signal anyway.

For critical standby power, Exelon depends on eight Fairbanks Morse Opposed Piston 38D 8 1 / 8 Emergency Diesel Generator sets that deliver 26 MW of power and are capable of achieving rated speed within ten seconds of start.

Radio receiver manufacturers concentrated on FM and AM-MW bands, with fewer and fewer radio sets capable of receiving Long wave at all, and most of those that did having very poor audio.

For ease of maintenance, availability of spare parts and increased reliability, two sets of Walschaerts valve gear were used, along with the largest cylinders capable of staying within the British loading gauge.

Some newer versions of pppd are also capable of handling Dial-on-demand routing, where pppd sets up a virtual network, captures the packages it receives and establishes a PPP connection and forwards the captured and not-yet transmitted packages over the link.

Althea sets off to prove she is a capable sailor.

DR is funded by the levying of a broadcast receiving licence fee, payable in Denmark by all owners of radios, television sets, and, in recent years, computers and other devices capable of receiving DR's video content, whether or not they use DR's services.