A converse to completeness is soundness, the fact that only logically valid formulas are provable in the deductive system.

A converse to completeness is soundness, the fact that only logically valid formulas are provable in the deductive system.

Again, converse to popular knowledge, the " shadow " is not the remains or ash of the victim, but in fact it was the area around the shadow, not obscured by the person's silhouette that was lightened by X-rays from the burst, leaving a dark " negative " shadow.

Beethoven used to say ...' They who thoroughly study Clementi, at the same time make themselves acquainted with Mozart and other composers ; but the converse is not the fact.

The converse is not true ; in fact, in a certain sense, the analytic functions are sparse compared to all infinitely differentiable functions.

However, it also shows that the compactness of the product of compact Hausdorff spaces can be proved using ( BPIT ), and in fact the converse also holds.

One reason for the trust he enjoyed from King George was the fact that they could converse in German, which he spoke fluently.

Caution: The converse of Whitehead's problem, namely that every free abelian group is Whitehead, is a well known group-theoretical fact.

In fact, utilizing the holomorphic version of the Poincaré lemma, a partial converse holds true locally.

The two arguments imply there is no difference between the exception and the rule, and in fact fallacious slippery slope arguments often use the converse accident to the contrary as the basis for the argument.

Cardinal electors may not correspond or converse with anyone outside the conclave, by post, radio, telephone or otherwise and eavesdropping is an offense punishable by excommunication latae sententiae — in fact, before the conclave that elected Pope Benedict XVI, the Sistine Chapel was " swept " using the latest electronic devices to detect any hidden " bugs " or surveillance devices ( there were no reports that any were found, but in previous conclaves there were discovered press reporters who had disguised themselves as conclave servants ).

In fact, to compute Tor ( A, B ), one may use a flat resolution of A or B, instead of a projective resolution ( note that a projective resolution is automatically a flat resolution, but the converse isn't true, so allowing flat resolutions is more flexible ).

In fact, if the ratio test works ( meaning that the limit exists and is not equal to 1 ) then so does the root test ; the converse, however, is not true.

The converse of this fact is only partially true,

In fact each faithful-module is a faithful representation of G, but the converse does not hold.

In fact, one important aspect of their very religion is the annihilation of men ''.

In fact it has caused us to give serious thought to moving our residence south, because it is not easy for the most objective Southerner to sit calmly by when his host is telling a roomful of people that the only way to deal with Southerners who oppose integration is to send in troops and shoot the bastards down.

The fact is due mainly to international wars, both hot and cold.

While the pattern is uneven, some having gained more than others, nationalism has in fact served the Western peoples well.

In point of fact, this is a beige box with a bright red door, about one and a half feet square and hung from the wall about six feet from the door to Wisman's right.

The fact is that the Southern Confederacy differed from the earlier one almost as much as the Federal Constitution did.

To my knowledge, Lincoln remains the only Head of State and Commander-in-Chief who, while fighting a fearful war whose issue was in doubt, proved man enough to say this publicly -- to give his foe the benefit of the fact that in all human truth there is some error, and in all our error, some truth.

In fact the accumulation of the hardware of destruction is day by day increasing our fear of each other.

The new fact the initiates of this cult have to learn is that they must move toward simplicity.

The magic circle is, in fact, a symbol of and preparation for the metaphysical orgasm ''.

Operating as a one man police force in fact if not in name, he is at once more independent and more dedicated than the police themselves.

`` I may possibly be a greater risk than is the normal person of my age '', the President had said on February 29th of the election year, ignoring the fact that no one of his age had ever lived out another term.

In the incessant struggle with recalcitrant political fact he learns to focus the essence of a problem in the significant detail, and to articulate the distinctions which clarify the detail as significant, with what is sometimes astounding rapidity.

we accord it its place there, and in Lawrence's treatment we are given the innocent fantasy of a child, in fact, the form in which oedipal love is expressed in childhood.

There is probably some significance in the fact that two of the best incest stories I have encountered in recent years are burlesques of the incest myth.

How much they esteemed him is shown by the fact that their underground committee selected him as one of the few who would be helped to escape.

That is not to deny that he has been aware of traditions, of course, that he is steeped in them, in fact, or that he has dealt with them, in his books.

There is evidence to suggest, in fact, that many authors of the humorous sketches were prompted to write them -- or to make them as indelicate as they are -- by way of protesting against the artificial refinements which had come to dominate the polite letters of the South.

It seems quite obvious that all the really difficult tasks of human beings arise from the fact that man is not one, but many.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

Perhaps the mere fact that by plucking on the nerves nature can awaken in the most ordinary of us, temporarily anyway, the sleeping poet, and in poets can discover their immortality, is the most remarkable of all the remarkable phenomena to which we can attest??

It was also subtly familiar, for it was the odor of the human body, but multiplied innumerable times because of the fact that the aborigines never bathed.

We are also struck by the fact that this story of a boy's love for his mother does not offend, while the incestuous love of the man, Paul Morel, sometimes repels.

He also disliked Runyon, for no good reason other than the fact that the Demon's talent was so marked as to put him well beyond the Hetman's say-so or his supervision.

This finding is consistent also with the fact that student leaders are more likely to be supporters of the values implicit in civil liberties than the other students.

And it is also a fact of life that there will always ( be youngish half-educated people around, who will be dazzled by the glitter of what looks like a literary movement.

But Schnabel was a great teacher in addition to being a great performer, and the fact that four of the ten versions I listened to are by Schnabel pupils ( Clifford Curzon, Frank Glazer, Adrian Aeschbacher, and Victor Babin ) also sheds light on the master's pedagogical skills.

Perhaps a clue to these and related problems lies in the fact that changes in the intensity of hypothalamic discharges which are associated with changes in its balance lead also to qualitative alterations in reactivity.

The unifying effect of religion is also brought out in the fact that historically peoples have clung together as more or less cohesive cultural units, with religion as the dominant bond, even though spatially dispersed and not politically organized.

We are abstracting from the fact of strikes here, but it should be obvious that the extent to which the public-limit price is raised by a given increase in the basic wage rate is also a function of the show of resistance put up by the industry.

In fact, a cash purchase of a corporation's stock followed by liquidation might also be an effective way to transfer a claim for refund if the Kimbell-Diamond doctrine is not applied to eliminate the intermediate step.

It also overlooks the fact that in a rational lexicon, and quite clearly in More's lexicon, the opposite of serious is not gay but frivolous, and the opposite of gay is not serious but solemn.

The need that we not give unqualified approval to any but a limited use of economic pressure directed against the actual doers of injustice is clear also in light of the fact that White Citizens' Councils seem resolved to maintain segregation mainly by the use of these same means and not ordinarily by physical violence.

A certain vagueness may also be caused by tactical appreciation of the fact that the present council meeting is a semipublic affair, with no fewer than six Soviet correspondents accredited.

There was also the fact that by the time he meets Mr. Khrushchev, the President will have completed conversations with all the other principal Allied leaders.

Although I have emphasized the barriers which an aroused nationalism has raised against relations between Christians and non-Christians in Asia, the fact is that this development has also widened the gulf between certain Afro-Asian religions themselves.

This is usually done on the basis that the lower court judge erred in the application of law, but it may also be possible to appeal on the basis of court misconduct, or that a finding of fact was entirely unreasonable to make on the evidence.

Swift also recognizes the implications of such a fact in making mercantilist philosophy a paradox: the wealth of a country is based on the poverty of the majority of its citizens.

Swift however, Landa argues, is not merely criticizing economic maxims but also addressing the fact that England was denying Irish citizens their natural rights and dehumanizing them by viewing them as a mere commodity.

It has been said that twelve cases related in The Labours of Hercules ( 1947 ) must refer to a different retirement, but the fact that Poirot specifically says that he intends to grow marrows indicates that these stories also take place before Roger Ackroyd, and presumably Poirot closed his agency once he had completed them.

The sum, difference, product and quotient of two algebraic numbers is again algebraic ( this fact can be demonstrated using the resultant ), and the algebraic numbers therefore form a field, sometimes denoted by A ( which may also denote the adele ring ) or < span style =" text-decoration: overline ;"> Q </ span >.

Adventists also point to the fact that the wage of sin is death and God alone is immortal.

For example, automobile wheels made of an aluminium alloy are commonly referred to as simply " alloy wheels ", although in point of fact steels and most other metals in practical use are also alloys.

However, Robert Rines, who previously made two underwater photographs allegedly showing the monster, countered with the fact that they can also be arranged into " Yes, both pix are monsters, R ."

Rhoticity was further supported by Hiberno-English, West Country English and Scottish English as well as the fact most regions of England at this time also had rhotic accents.

First: it " mandates that whoever is the sovereign of the United Kingdom is also, by virtue of this external fact, sovereign of Australia "; accordingly, changes to British succession laws would have no effect on Australian law, but if the British amendment changed the sovereign, then the new sovereign of the United Kingdom would automatically become the new sovereign of Australia.