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Page "Constructivism (mathematics)" ¶ 14
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fact and standard
In cases where a judge rather than a jury decided issues of fact, an appellate court will apply an " abuse of discretion " standard of review.
The fact that the Aeginetan standard of weights and measures ( developed in the mid-7th century ) was one of the two standards in general use in the Greek world ( the other being the Euboic-Attic ) is sufficient evidence of the early commercial importance of the island.
Those who identify a particular dialect as the " standard " or " proper " version of a language are in fact using these terms to express a social distinction.
Cross-cultural psychiatrist Arthur Kleinman contends that the Western bias is ironically illustrated in the introduction of cultural factors to the DSM-IV: the fact that disorders or concepts from non-Western or non-mainstream cultures are described as " culture-bound ", whereas standard psychiatric diagnoses are given no cultural qualification whatsoever, is to Kleinman revelatory of an underlying assumption that Western cultural phenomena are universal.
Its persistence can probably be explained by the fact that it can be invoked to automatically perform small modifications on text files, by piping a script of commands to it through standard input.
It is important to distinguish between a secco work done on top of buon fresco, which according to most authorities was in fact standard from the Middle Ages onwards, and work done entirely a secco on a blank wall.
Because the vast majority of genes are encoded with exactly the same code ( see the RNA codon table ), this particular code is often referred to as the canonical or standard genetic code, or simply the genetic code, though in fact some variant codes have evolved.
Learners who wish to use purportedly correct English are in fact faced with the dual standard of American English and British English, and other less known standard Englishes ( including Australian, Scottish and Canadian ).
This has been said to be due to the fact that researchers in the past, such as Lamarck, viewed vertebrates as a " standard ": in Lamarck's theory of evolution, he believed that characteristics acquired through the evolutionary process involved not only survival, but also progression toward a " higher form ", to which humans and vertebrates were closer than invertebrates were.
The top quark, which he and other physicists realized must exist according to the standard model, was, in fact, produced at Fermilab not long after this book was published.
In fact, much analysis is devoted to cases where so-called market failures lead to resource allocation that is suboptimal by some standard ( defense spending is the classic example, profitable to all for use but not directly profitable for anyone to finance ).
What distinguishes these tasks from other potential and actual NLP tasks is not only the volume of research devoted to them but the fact that for each one there is typically a well-defined problem setting, a standard metric for evaluating the task, standard corpora on which the task can be evaluated, and competitions devoted to the specific task.
( This was in fact the label's standard practice until the mid-1980s.
Instead of using " that which promotes my ( human ) life " as his standard of value, he mistakes " that which I ( mindlessly happen to ) value " for a standard of value, in contradiction of the fact that, existentially, he is a human and therefore rational organism.
This vacillation between meter and word stress highlights the fact that Latin literature was still in its infancy, and that there was not yet a standard way to write verse.
Although Orbison recorded and wrote standard structure songs before " Only the Lonely ", he claimed never to have learned how to write them: " I'm sure we had to study composition or something like that at school, and they'd say ' This is the way you do it ,' and that's the way I would have done it, so being blessed again with not knowing what was wrong or what was right, I went on my own way .... So the structure sometimes has the chorus at the end of the song, and sometimes there is no chorus, it just goes ... But that's always after the fact — as I'm writing, it all sounds natural and in sequence to me.
Today most American stock cars may superficially resemble standard American family sedans, but are in fact purpose-built racing machines built to a strict set of regulations governing the car design ensuring that the chassis, suspension, engine, etc.
Truth is most often used to mean in accord with fact or reality or fidelity to an original or to a standard or ideal.
In spite of the fact that the decreed definition of the gram specified water at 0 ° C — a highly reproducible temperature — the scientists chose to redefine the standard and to perform their measurements at the temperature of highest water density, which was measured at the time as.
This traditional name continues as the standard in the United States, although it obscures the fact that Indians fought on both sides of the conflict.
As the Tandy 1000 line outlasted the PCjr by many years ( and in fact did not make it to market until shortly before IBM announced the discontinuation of the PCjr ) these graphics and sound standards became known as " Tandy-compatible " or ( for the graphics ) " TGA " ( standing for Tandy Graphics Adapter ) and many software packages of the era listed their support for Tandy standard hardware on the package.

fact and constructive
And in fact, Cantor's diagonal argument is constructive, in the sense that given a bijection between the real numbers and natural numbers, one constructs a real number which doesn't fit, and thereby proves a contradiction.
When the negative team appeals to prima facie, it appeals to the fact that the affirmative team cannot add or amend anything in its plan after being stated in the first affirmative constructive.
In fact, the Disquisitiones contains two proofs: the one in Article 54 is a nonconstructive existence proof, while the other in Article 55 is constructive.
However, in the course of a few years, he came to feel that nothing constructive was to be accomplished by remaining at Point Loma — that, in fact, the teachings and philosophy of Theosophy had suffered an almost complete eclipse by the methods and sensational program instituted by Mrs. Tingley — and he quietly left the Point Loma Society in 1904 and came to Los Angeles.
In that book, the talk is about constructive mathematics ; but in fact this can be read as foundational computer science ( which is not mentioned ).
Motion is the fundamental fact common to being and thought ; the actual motion of the external world has its counterpart in the constructive motion involved in every instance of perception or thought.
In 1996 Lubich was awarded the UNESCO Prize for education to peace, in Paris, motivated by the fact that, " in an age when ethnic and religious differences too often lead to violent conflict, the spread of the Focolare Movement has also contributed to a constructive dialogue between persons, generations, social classes and peoples.
" Paraphrased Sony into its own words, the Ninth Circuit explained that if a defendant " made and sold equipment capable of both infringing and substantial noninfringing uses ," that fact alone — i. e., " evidence that such machines could be and were used to infringe plaintiffs ' copyrighted television shows " – would not be sufficient grounds to impute constructive knowledge to defendants.
Terence Reese said " The Official System ( Lenz )... was discredited ... That the Culbertsons did not win more easily ( for their constructive bidding was much better than that of their opponents ) was due to the fact that Jacoby was a player of quite different class from any of the others ".

fact and interpretation
According to the official interpretation of the Charter, a member cannot be penalized by not having the right to vote in the General Assembly for nonpayment of financial obligations to the `` special '' United Nations' budgets, and of course cannot be expelled from the Organization ( which you suggested in your editorial ), due to the fact that there is no provision in the Charter for expulsion.
This fact is of difficult interpretation.
This interpretation is now generally discarded, as Poseidonios ' narrative makes it more likely that the country some of the Helvetians left in order to join in the raids of the Teutones, Cimbri, and Ambrones was in fact southern Germany and not Switzerland.
Complicating this process is the fact that Suber's initial ruleset allows for the appointment of judges to preside over issues of rule interpretation.
" A complete system of outcomes for a subject area normally includes everything from mere recitation of fact (" Students will name three tragedies written by Shakespeare ") to complex analysis and interpretation (" Student will analyze the social context of a Shakespearean tragedy in an essay ").
Statements which entail an interpretation of fact are not perjury because people often draw inaccurate conclusions unwittingly, or make honest mistakes without the intent to deceive.
The fact that the rubaiyat are a collection of quatrains-and may be selected and rearranged subjectively to support one interpretation or another-has led to widely differing versions.
This experiment makes apparent the fact that the nature of measurement, or observation, is not well-defined in this interpretation.
In the Early Christian Church, the presumed fact was that the Septuagint was translated by Jews before the era of Christ, and that the Septuagint at certain places gives itself more to a christological interpretation than ( say, 2nd century ) Hebrew texts, was taken as evidence, that " Jews " had changed the Hebrew text in a way that made them less christological.
" ( Although the " reduction " mentioned is spurious as the two diagrams 3. 4 and 3. 5 are in fact the same ) and also " As we will see on the next few pages, the look-across interpretation introduces several difficulties which prevent the extension of simple mechanisms from binary to n-ary associations.
In fact, the modern explanation of the uncertainty principle, extending the Copenhagen interpretation first put forward by Bohr and Heisenberg, depends even more centrally on the wave nature of a particle: Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions ; likewise, just as it is nonsensical to discuss the wavelength of a " pulse " wave traveling down a string, particles do not have perfectly precise momenta ( which corresponds to the inverse of wavelength ).
This is the interpretation offered by William himself in the Historia, and it was taken as fact by later historians.
" As mentioned above, William was opposed to Baldwin's mother Agnes of Courtenay, Patriarch Heraclius, and their supporters ; his interpretation of events during Baldwin's reign was previously taken as fact almost without question.
In fact, Hubble was clear from the beginning that no such interpretation was implied:
Thus it would seem that Lewis Carroll did not intend care and hope from the repeating stanza to stand for two women, but was quite pleased with the interpretation after the fact.
In fact, the wave aspect of matter was formalized by a wavefunction defined by the Schrödinger equation, which is a pure mathematical entity having a probabilistic interpretation, without the support of real physical elements.
The Copenhagen interpretation states that the particles are not localised in space until they are detected, so that, if there is not any detector on the slits, there is no matter of fact about which slit the particle has passed through.
# they are interpretations of a phenomenology, a set of observations, including both those obtained by empirical research, and more informal subjective ones ( the fact that humans invariably observe an unequivocal world is important in the interpretation of quantum mechanics ).
The values shown in the cells of the table are not without controversy, for the precise meanings of some of the concepts involved are unclear and, in fact, are themselves at the center of the controversy surrounding the given interpretation.
This interpretation is flawed by the fact it relies on a very odd reading of " good a will " to mean " incorrect judgements " rather than the more intuitive " good intentions.
This has now been widely acknowledged as a fact by studies of the period, what is still wide open to interpretation is the " how and why " that happened.
Alexandrian scholars in fact interpreted a number of passages in Pindar as hostile allusions to Bacchylides and Simonides and this interpretation has been endorsed by modern scholars also.
In fact, the specific nature of the MacGuffin may be ambiguous, undefined, generic, left open to interpretation or otherwise completely unimportant to the plot.
Another interpretation is that the portrait is in fact a mirror, and that the painting itself is in the perspective of the King and Queen, hence their reflection can be seen in the mirror on the back wall.

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