Thus, in order to show that any axiomatic system of mathematics is in fact consistent, one needs to first assume the consistency of a system of mathematics that is in a sense stronger than the system to be proven consistent.

Introduction to Objectivist Epistemology describes axiomatic concepts as " the identification of a primary fact of reality, which cannot be analyzed, i. e., reduced to other facts or broken into component parts ".

Married persons who are known to commit such acts may in fact lose privileges in the congregation as they are supposed to be setting a good example to the congregation.

Posted flamebait can provide the poster with a controlled trigger-and-response setting in which to anonymously engage in conflicts and indulge in aggressive behavior without facing the consequences that such behavior might bring in a face-to-face encounter, a fact parodied in a YouTube video by Isabel Fay.

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.

One fact which complicates discussion of the Patterson film is that Patterson says he normally filmed at 24 frames per second, but in his haste to capture the Bigfoot on film, he did not note the camera's setting.

In that episode, Scotty implied that he believed Kirk to still be alive, despite the fact that the scene's setting was after Scotty had witnessed Kirk's apparent death in Star Trek: Generations.

This was, in fact, the setting of Ricci's original work.

The diversity of the regions is in fact the most pronounced attribute of Thailand's physical setting.

In fact, there was a total eclipse of the sun in the Aegean on March 5, 1223 BC, which Atreus might have twisted into a setting of the sun in the east.

*" George W. Bush has a vision which can be described with two other words: Manichaean paranoia ... the notion that he is leading the forces of good against the empire of evil, that in that setting, the fact that we are morally superior justifies us committing immoral acts.

Language is also important in relation to Tranio and Lucentio, who appear on stage speaking a highly artificial style of blank verse full of classical and mythological allusions and elaborate metaphors and similes, thus immediately setting them aside from the more straightforward language of the Induction, and alerting the audience to the fact that we are now in an entirely different milieu.

The setting of the story is in fact the very real Tuscan area of Italy as a background.

Mana is a limited resource in Niven's work, a fact which eventually will lead to the end of all magic in his antediluvian fantasy setting when all mana is depleted.

The fact that, in some of the literature concerning Gawain, his strength waxes and wanes with the rising and setting of the sun is indicative of this analogy, and suggests an Irish rather than a Welsh origin.

The main reason for the film's setting is the fact that the Coens were born and raised in St. Louis Park, a suburb of Minneapolis.

Besides the chapel, it contains the Sängersaal ( Hall of the Minstrels ), which is in fact Wagner's setting for Act II of Tannhäuser and the Festsaal ( the Feast or Festival Hall ), both of which contain fine frescoes by Moritz von Schwind with the theme of the minstrels ' contest in the Sängersaal and frescoes of the triumphs of Christianity in the Festsaal.

In fact there is little trace of Machiavelli in French writings before the massacre, and not very much after, until Gentillet's own book, but this concept was seized upon by many contemporaries, and played a crucial part in setting the long-lasting popular concept of Machiavellianism that so infuriates scholars of his actual thought.

Although the setting of The Mary Tyler Moore Show might have implied that he was a native Minnesotan, Lou Grant in fact established that he was born in the fictional town of Goshen, Michigan.

The very first of what would become more than 400 in the state, the SFCBC was a three-story full service medical marijuana club where qualified patients could in fact obtain marijuana for medical purposes ( in various forms and qualities ) in a retail setting.

Spencer, in fact, went further than most of his ministerial colleagues, including Gladstone himself, in arguing for the setting up of government tribunals to enforce fair rents on Irish landlords.

The Lacandón became associated as being isolated from other groups, a fact which was facilitated largely by the geographical setting in which they lived.

He also seems to have borrowed the main setting of his novella On Chesil Beach ( 2005 ) from Dover Beach, additionally playing with the fact that Arnold's poem was composed on his honeymoon ( see above ).

Another upshot of the fact that the graphics were rendered rather than simple images is that while the sun was setting, the entire palette of colors changed convincingly.

The Irish media made much tongue-in-cheek mention of the fact that the disaster occurred on Friday the 13th, a date often linked to supposed curses and disasters and also the fact that the ship's name had been changed for the programme: sailing lore suggests that any ship which is renamed prior to setting sail will meet with disaster.

The scripting team added the tennis match — and the crosscutting with Bruno's storm drain travails in Metcalf — added the cigarette lighter, the Tunnel of Love, Miriam's eyeglasses ; in fact, the amusement park is only a brief setting in the novel.

In fact, mathematical induction is a form of rigorous deductive reasoning.

Again, a rigorous proof is needed for the fact that does not admit an equivalent regular expression of lower star height.

It is well known for its illustrated and often topical covers, its commentaries on popular culture and eccentric Americana, its attention to modern fiction by the inclusion of short stories and literary reviews, its rigorous fact checking and copyediting, its journalism on politics and social issues, and its single-panel cartoons sprinkled throughout each issue.

Also, rigorous scientific use of the term " fact " is careful to distinguish: 1 ) states of affairs in the external world ; from 2 ) assertions of fact that may be considered relevant in scientific analysis.

In fact, the vast majority of proofs in written mathematics can be considered as applications of rigorous informal logic.

In fact, the other techniques can be seen as special cases of stemmatics in which a rigorous family history of the text cannot be determined but only approximated.

However, the first mathematically rigorous proof of this fact was obtained only in the 19th century.

Both the rigorous journalistic standards and the fact that it was the first Spanish newspaper to establish internal quality control standards have increased the standing of El País.

Community informatics would in fact probably benefit from closer knowledge of, and relationship to, theorists, practitioners, and evaluators of rigorous qualitative research and practice.

The fact remains that the MMA ’ s political experience derived from establishing street power, however translating such into a coherent, effective ideology was precarious, and thus was exposed by the accountable, rigorous forces of the democratic process.

Exactly like the natural sciences, as opposed to the Social Sciences where claims can be reduced to fact, rigorous approach is seen as hard work, not polemicist point scoring and guess work.

However, a more rigorous analysis calculates the limit to be Z ≈ 173, indicating that unsepttrium ( element 173 ) is in fact the last possible neutral atom.

) In fact Killing's work was less rigorous logically than Lie's, but Killing had much grander goals in terms of classification of groups, and made a number of unproven conjectures that turned out to be true.

The mere fact that a theory has survived the most rigorous empirical tests available does not, in the calculus of probability, predict its ability to survive future testing.

As Poe wrote in a letter in 1842: " under the pretense of showing how Dupin ... unravelled the mystery of Marie's assassination, I, in fact, enter into a very rigorous analysis of the real tragedy in New York ".