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( valid for any elements x, y of a commutative ring ),
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valid and for
And although these insights into the nature of art may be in themselves insufficient for a thoroughgoing philosophy of art, their peculiar authenticity in this day and age requires that they be taken seriously and gives promise that from their very substance, new and valid chapters in the philosophy of art may be written.
On the other hand, the consensus of opinion is that, used with caution and in conjunction with other types of evidence, the native sources still provide a valid rough outline for the English settlement of southern Britain.
If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.
In general, it appears that trustees and board members attempt to represent the public interest in their administration of educational policy, and this is made easier by the fact that the dominant values of the society are middle-class values, which are generally thought to be valid for the entire society.
-- On the basis of a differentiability assumption in function space, it is possible to prove that, for materials having the property that the stress is given by a functional of the history of the deformation gradients, the classical theory of infinitesimal viscoelasticity is valid when the deformation has been infinitesimal for all times in the past.
The evidence shows that fake therapeutic machines, substituted for valid medical cures, have hastened the deaths of thousands.
Despite these facts, most mathematicians accept the axiom of choice as a valid principle for proving new results in mathematics.
The author's name " indicates the status of the discourse within a society and culture ", and at one time was used as an anchor for interpreting a text, a practice which Barthes would argue is not a particularly relevant or valid endeavor.
As for the term " Compositae ", more ancient but still valid, it obviously makes reference to the fact that the family is one of the few angiosperms that have composite flowers.
Not only was his Belgian nationality interesting because of Belgium's occupation by Germany ( which provided a valid explanation of why such a skilled detective would be out of work and available to solve mysteries at an English country house ), but also at the time of Christie's writing, it was considered patriotic to express sympathy with the Belgians, since the invasion of their country had constituted Britain's casus belli for entering World War I, and British wartime propaganda emphasized the " Rape of Belgium ".
Use of the term to describe writers, for example, is certainly valid, but less common, and mostly restricted to contexts like criticism.
In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.
While it would be rash to assert positively that no existing gems were the work of Gnostics, there is no valid reason for attributing any or all of them to such an origin.
NANPA's utilised codes report will indicate ' UA ' ( unassignable ) for valid test prefixes ; if a formerly ' UA ' code newly appears on the available list or becomes an active exchange, any former test numbers from its time as a reserved prefix are presumable as invalid and deprecated.
" In the 1999 South Carolina Supreme Court case State v. Gaines, the Court held that Alford guilty pleas were to be held valid in the absence of a specific on-the-record ruling that the pleas were voluntary – provided that the sentencing judge acted appropriately in accordance with the rules for acceptance of a plea made voluntarily by the defendant.
* The being which manifests in Christianity also manifests in all faiths and religions, and each religion is valid and true for the time and cultural context in which it was born ;
The " heuristic " approach of the Logic Theory Machine tried to emulate human mathematicians, and could not guarantee that a proof could be found for every valid theorem even in principle.
This is the most natural configuration for memory, as all combinations of their address lines map to a valid address, allowing easy aggregation into a larger block of memory with contiguous addresses.
The Catholic Church does recognise as valid ( though illicit ) ordinations done by breakaway Catholic, Old Catholic or Oriental bishops, and groups descended from them ; it also regards as both valid and licit those ordinations done by bishops of the Eastern churches, so long as those receiving the ordination conform to other canonical requirements ( for example, is an adult male ) and an orthodox rite of episcopal ordination, expressing the proper functions and sacramental status of a bishop, is used ; this has given rise to the phenomenon of episcopi vagantes ( for example, clergy of the Independent Catholic groups which claim apostolic succession, though this claim is rejected by both Orthodoxy and Catholicism ).
valid and any
* In a version of Scrabble called Clabbers, the name itself being an anagram of Scrabble, tiles may be placed in any order on the board as long as they anagram to a valid word.
For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.
The Holy See accepts as valid the ordinations of the Old Catholics in communion with Utrecht, as well as the Polish National Catholic Church ( which received its orders directly from Utrecht, and was — until recently — part of that communion ); but Roman Catholicism does not recognise the orders of any group whose teaching is at variance with what they consider the core tenets of Christianity ; this is the case even though the clergy of the Independent Catholic groups may use the proper ordination ritual.
A prefix code is a code with the " prefix property ": there is no valid code word in the system that is a prefix ( start ) of any other valid code word in the set.
During any shot, any disc that falls completely into the recessed central " 20 " hole ( aka the " Toad ") is removed from play, and counts as twenty points for the owner of the disc at the end of the round, assuming the shot is valid.
Thus, to be valid, any law must conform to natural law and coercing people to conform to that law is morally acceptable.
It is binding over all the globe, in all countries, and at all times: no human laws are of any validity, if contrary to this ; and such of them as are valid derive all their force, and all their authority, mediately or immediately, from this original.
This view entails the problem that it makes any moral criticism of the law impossible: if conformity with natural law forms a necessary condition for legal validity, all valid law must, by definition, count as morally just.
However it is important to note that the objects of a category need not be sets nor the arrows functions ; any way of formalising a mathematical concept such that it meets the basic conditions on the behaviour of objects and arrows is a valid category, and all the results of category theory will apply to it.
Stove alleged that by using weak or false ad hoc reasoning, these Ultra-Darwinists used evolutionary concepts to offer explanations that were not valid ( e. g., Stove suggested that sociobilogical explanation of altruism as an evolutionary feature was presented in such as way that the argument was effectively immune to any criticism.
Note that any valid SGML or XML document that references an external subset in its DTD, or whose body contains references to parsed external entities declared in its DTD ( including those declared within its internal subset ), may only be partially parsed but cannot be fully validated by validating SGML or XML parsers in their standalone mode ( this means that these validating parsers will not attempt to retrieve these external entities, and their replacement text will not be accessible ).
He also presents an argument against qualia ; he argues that the concept is so confused that it cannot be put to any use or understood in any non-contradictory way, and therefore does not constitute a valid refutation of physicalism.
Consequentialism refers to moral theories that hold that the consequences of a particular action form the basis for any valid moral judgment about that action ( or create a structure for judgment, see rule consequentialism ).
The tradition built by those legends has chosen to recognize just the putative male ancestry as valid for legitimizing his succession, not giving any weight to ties through the said princesses.
It assumes that the call arrivals may be modeled by a Poisson process, but is valid for any statistical distribution of call holding times with finite mean.
valid and elements
The set of valid index tuples and the addresses of the elements ( and hence the element addressing formula ) are usually, but not always, fixed while the array is in use.
It is " one of four elements which define the true Church of Jesus Christ " and legitimizes the ministry of its clergy, as only a bishop within the succession can perform legitimate or " valid " ordinations.
He was aware that the Council of Jamnia, or mainstream rabbinical Judaism, had rejected the Septuagint as valid Jewish scriptural texts because of what were ascertained as mistranslations along with its Hellenistic heretical elements.
Nonetheless, many elements of the theory are still believed to be valid, or the theory is presented in a non-Marxist tradition.
These elements concorded suggestively with those made independently by another astronomer named David Peck Todd, suggesting to many that they might be valid.
Eastern Orthodox, Oriental Orthodox, and Roman Catholics, who together constitute the majority of Christians, hold that the consecrated elements in a valid celebration of the Eucharist indeed become the body and blood of Christ.
Given any such interpretation of a set of points as complex numbers, the points constructible using valid compass and straightedge constructions alone are precisely the elements of the smallest field containing the original set of points and closed under the complex conjugate and square root operations ( to avoid ambiguity, we can specify the square root with complex argument less than π ).
Thus a particular coordinate system ( equinox and equator / ecliptic of a particular date, such as J2000. 0 ) could be used forever, but a set of osculating elements for a particular epoch may only be ( approximately ) valid for a rather limited time, because osculating elements such as those exampled above do not show the effect of future perturbations which will change the values of the elements.
The elements of a valid cause of action for abuse of process in most common law jurisdictions are as follows: ( 1 ) the existence of an ulterior purpose or motive underlying the use of process, and ( 2 ) some act in the use of the legal process not proper in the regular prosecution of the proceedings.
In religion, Eclectics use elements from multiple religions, applied philosophies, personal experiences or other texts and dogma to form their own beliefs and ideas, noting the similarities between existing systems and practices, and recognizing them as valid.
Other parts of the extensive work of Snorri Sturluson ( and other saga writers ) may however be considered valid references for finding elements of the ancient history of Scandinavian people and their religious customs and beliefs.
These customs indeed do have more than a few elements of pre-Christian beliefs, but simply inventing gods based on names of customs is not considered a valid method for reconstruction of lost beliefs.
A valid Catholic marriage results from four elements: ( 1 ) the spouses are free to marry ; ( 2 ) they freely exchange their consent ; ( 3 ) in consenting to marry, they have the intention to marry for life, to be faithful to one another and be open to children ; and ( 4 ) their consent is given in the presence of two witnesses and before a properly authorized Church minister.
In other words, the elements of geometry form a system which is not susceptible of extension, if we regard the five groups of axioms as valid.
Because even satellites in low earth orbit experience significant perturbations ( primarily from the non-spherical shape of the earth ), the Keplerian elements computed from the state vector at any moment are only valid at that time.
In order to create something rooted in his own Japanese culture and history but still fresh and valid internationally, he began searching for something that could be considered ‘ uniquely Japanese .’ After concluding that elements of ‘ high ’ art were confounding at best, he began to focus on Japan ’ s ‘ low ’ culture, especially anime and manga, and the larger subculture of otaku.
At the latter Council the Greeks admitted the Latin contention that the consecration of the elements was equally valid with leavened and unleavened bread ; it was decreed that the priests of either rite should conform to the custom of their respective Church.
This example contains all the elements of a valid authority record: the first heading is the form of the name that the Library of Congress has chosen to be authoritative.
Professionals developing certification exams use job analysis ( often called something slightly different, such as " task analysis " or " work analysis ") to determine the elements of the domain which must be sampled in order to create a content valid exam.