The mandate is distinguished from the appeal court's opinion, which sets out the legal reasoning for its decision.

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 of his theological textbooks that strove to be more minute in its focus, is his De Fide Catholica, dated somewhere between 1185 to 1200, Alan sets out to refute heretical views, specifically that of the Waldensians and Cathars.

" It ends in death, and sets the stage for an album populated by rogues, con men, outcasts, gamblers, gunfighters and desperados, many of them with nothing to lose, some of them out of their minds, all of them quintessentially American.

For example, in the United Kingdom, the Companies Act 2006 requires directors of companies " to promote the success of the company for the benefit of its members as a whole " and sets out the following six factors regarding a director's duty to promote success:

As it turned out, assuming that one can perform any operation on sets without restriction leads to paradoxes such as Russell's paradox and Berry's paradox.

" He then had sets constructed and worked with his stock company to improvise gags and " business " around them, almost always working the ideas out on film.

This allows weather and lighting to be controlled ( as the shooting is indoors ), and for all clothing and sets to be stored in one place to be hauled out the next day from a secure location.

Nonetheless, it turns out that infinite sets do have a well-defined notion of size ( or more properly, of cardinality, which is the technical term for the number of elements in a set ), and not all infinite sets have the same cardinality.

The convention reminds decision-makers that natural resources are not infinite and sets out a philosophy of sustainable use.

The Nagoya Protocol sets out core obligations for its contracting Parties to take measures in relation to access to genetic resources, benefit-sharing and compliance.

Her father then sets out with Laura in a carriage for the ruined village of Karnstein.

In legal terminology, a complaint is any formal legal document that sets out the facts and legal reasons ( see: cause of action ) that the filing party or parties ( the plaintiff ( s )) believes are sufficient to support a claim against the party or parties against whom the claim is brought ( the defendant ( s )) that entitles the plaintiff ( s ) to a remedy ( either money damages or injunctive relief )

With this knowledge and a pair of glasses given to him as a gift by Wonder Woman, ' Clark ' regains his humanity, and sets out to become a hero again by re-fertilizing the irradiated fields of Kansas.

A brute-force approach converts these congruences into sets and writes the elements out to the product of ( the solutions modulo 60 for each congruence ):

Ironically, although the ID tags include religion as a way of ensuring that religious needs will be met, some personnel have them reissued without religious affiliation listed — or keep two sets, one with the designation and one without — out of fear that identification as a member of a particular religion could increase the danger to their welfare or their lives if they fell into enemy hands.

He sets out in the early morning and ends up at an inn, which he believes to be a castle.

* 1577 – Sir Francis Drake sets out from Plymouth, England, on his round-the-world voyage.

This would be an irresponsible act of reading because it ignores the empirical facticity of the text itself-that is it becomes a prejudicial procedure that only finds what it sets out to find.

Many of the Articles in Section I are structured in two paragraphs: the first sets out a basic right or freedom ( such as Article 2 ( 1 ) – the right to life ) but the second contains various exclusions, exceptions or limitations on the basic right ( such as Article 2 ( 2 ) – which excepts certain uses of force leading to death ).

That declaration sets out three aims for the construction of another Europe: the total change of institutions to make them " fully democratic "; and breaking with " neo-liberal monetarist policies "; and a policy of co-development and equitable cooperation.

With this communication Epaphroditus sets out on his homeward journey ( 3. 28-29 ).

In the later Babylonian epic Enûma Eliš, Abzu, the " begetter of the gods ", is inert and sleepy but finds his peace disturbed by the younger gods, so sets out to destroy them.

This is not the most general situation of a Cartesian product of a family of sets, where a same set can occur more than once as a factor ; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all distinct sets in the family.

In most concrete settings, however, the objects will be sets with some additional structure and the morphisms will be functions preserving that structure.

In this case, is the smallest σ-algebra that contains the open intervals of R. While there are many Borel measures μ, the choice of Borel measure which assigns for every interval is sometimes called " the " Borel measure on R. In practice, even " the " Borel measure is not the most useful measure defined on the σ-algebra of Borel sets ; indeed, the Lebesgue measure is an extension of " the " Borel measure which possesses the crucial property that it is a complete measure ( unlike the Borel measure ).

The informal content of this naive set theory supports both the aspects of mathematical sets familiar in discrete mathematics ( for example Venn diagrams and symbolic reasoning about their Boolean algebra ), and the everyday usage of set theory concepts in most contemporary mathematics.

The Cuban government sets most prices and rations goods to citizens.

The most accessible example of a category is the category of sets, where the objects are sets and the arrows are functions from one set to another.

In general topological spaces, however, the different notions of compactness are not necessarily equivalent, and the most useful notion, introduced by Pavel Alexandrov and Pavel Urysohn in 1929, involves the existence of certain finite families of open sets that " cover " the space in the sense that each point of the space must lie in some set contained in the family.

In general topological spaces, however, the different notions of compactness are not equivalent, and the most useful notion of compactness — originally called bicompactness — involves families of open sets that " cover " the space in the sense that each point of the space must lie in some set contained in the family.

In the most general sense of the word, a cement is a binder, a substance that sets and hardens independently, and can bind other materials together.

Eisenhower, as well as the officers and troops under him, had learned valuable lessons in their previous operations, and their skill sets had all strengthened in preparation for the next most difficult campaign against the Germans – a beach landing assault.

Larger sets such as double-twenty-one can theoretically exist but are rarely seen in retail stores, as identifying the number of pips on each domino becomes difficult, and a double-twenty-one set would have 253 pieces, far more than is normally necessary for most domino games even with eight players.

The wind up is one of the most important aspects of the throw because it sets the tone for the entire throw.

Although the wind up sets the tone for the entire throw, the rhythm of the throw is the most important aspect.

Hank Williams III's bass players ( Joe Buck and Zach Shedd, most notably ) have used upright basses for recording as well as during the country and Hellbilly sets of Hank III's live performances before switching to electric bass for the Assjack set.

He added that several engineers described the invention " as one of the most important radio developments since the first earphone crystal sets were introduced.

As a result, most investors will not commit to financing a film unless an insurer can be found to protect them against the risk that the film ultimately cannot be released as a result of a total catastrophe such as total loss of film negatives ( or digital media ), death of the Director or Stars during production, natural disasters destroying the sets, and so on.

Caprino directed and animated ; Bjarne Sandemose ( Caprino's principal collaborator throughout his career ) built most of the props, sets and cars and was in charge of the technical aspects of making the film ; Ingeborg Riiser designed the puppets and Gerd Alfsen made the costumes and props.

The most popular of the coin holders for date sets are coin albums.

* Size / Resize the case ( For previously fired cases, primer is pressed out in this step with most die sets.

Double-strung harps often have levers either on every string or on the most commonly sharped strings, for example C and F. Having two sets of strings allows the harpist's left and right hands to occupy the same range of notes without having both hands attempt to play the same string at the same time.

The distinction is used most often for sets that support both binary operations, such as rings.