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 sets out Nimzowitsch's most important ideas, while his second most influential work, Chess Praxis, elaborates upon these ideas, adds a few new ones, and has immense value as a stimulating collection of Nimzowitsch's own games accompanied by his idiosyncratic, hyperbolic commentary which is often as entertaining as instructive.

" 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.

Fifty lantern slide teaching sets on the subject of `` Emergency War Surgery ( NATO ) '' were assembled and distributed to the Medical Military Services of foreign Governments associated with NATO and South-East Asia Treaty Organization.

The demand for teaching sets continues unabated since they provide the means for the military physicians to review the pathology of selected disease processes or organ systems for review of basic sciences and correlation of clinical physiological behavior with structural changes.

Both home and auto radios were in excellent demand, with retail sales of home sets ahead of 1959 in every month of the first eleven ; ;

The last exercise of Roland Claude's prescribed program for Henri is a single exercise, done in individual sets with a bit longer pause between sets.

So with four complete Push-Pull Super-Sets No. 1, four of No. 2, four of No. 3 and four to six sets of the Incline Bench Press, you can see that Henri De Courcy has had a terrific mass-building, muscle-shaping, torso-defining workout that cannot be improved upon.

Squat-style lifters and leg-split lifters would both benefit enormously by practicing those variations providing that they remember to make alternate sets with the left and right leg to the front.

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

It was `` window '' -- the tinsel paper dropped by bombers to jam radar sets, to fill the scope with hundreds of blips that would seem to be approaching bombers.

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.

Compound comparisons typically compare two sets of groups means where one set has two or more groups ( e. g., compare average group means of group A, B and C with group D ).

: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

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.

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.

The same notation is used with sets to denote cardinality ; the meaning depends on context.

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

Articles of faith are sets of beliefs usually found in creeds, sometimes numbered, and often beginning with " We believe ...", which attempt to more or less define the fundamental theology of a given religion, and especially in the Christian Church.

In contrast, in the Arian German kingdoms established on the wreckage of the Western Roman Empire in the 5th century, there were entirely separate Arian and Nicene Churches with parallel hierarchies, each serving different sets of believers.