For example: in the First Antinomy, Kant proves the thesis that time must have a beginning by showing that if time had no beginning, then an infinity would have elapsed up until the present moment.

His thesis proves a conjecture by Edward Witten that two quantum gravitational models are equivalent.

If the candidate proves suitable and sufficiently knowledgeable a performance exam is scheduled or a thesis may be written.

In these essays, a 203-page masterpiece of objective critique, Hirsch proves beyond doubt that Graetz is guilty of the utmost sloppiness of scholarship: e. g., Graetz omitted the second halves of quotations which, if quoted in their entirety, flatly contradict his thesis.

This passion brings on a fit which proves fatal.

It resembles, too, pictures such as Durer and Bruegel did, in which all that looks at first to be solely pictorial proves on inspection to be also literary, the representation of a proverb, for example, or a deadly sin.

In spite of the armistice negotiated by Amadee two years earlier, the war between Bishop Guillaume of Lausanne and Louis of Savoy was still going on, and although little is known about it, that little proves that it was yet another phase of the struggle against French expansion and was closely interwoven with the larger conflict.

In the growing drug and pop culture of the sixties, he proves himself once again, but has become heavily reliant on other investigators ( especially the private investigator, Mr. Goby ) who provide him with the clues that he can no longer gather for himself.

If he himself philosopher did not exist, he would not be there to ask questions about the nature of reality ... on the other hand, this fundamental fact, which we call existence, soon proves a rather barren topic for philosophic speculation ...

He stated that " the fact that my name and address along with my picture can appear on the front of the papers before the so-called ' victim ' has even signed a statement proves that anonymity for rape defendants is a must and that the law must be changed.

But follow-up studies have ( depending on who was summarizing the results ) failed to replicate the phenomenon or produced mixed results ( Bem & others, 2001 ; Milton & Wiseman, 2002 ; Storm, 2000, 2003 ). One skeptic, magician James Randi, has a longstanding offer — now U. S. $ 1 million —“ to anyone who proves a genuine psychic power under proper observing conditions ” ( Randi, 1999 ).

Hayek's own words on democracy versus free market capitalism proves quite an insightful reading:

Bernard also adds his own ideas: the Ring Nebula proves the existence of hollow worlds, as well as speculation on the fate of Atlantis and the origin of flying saucers.

* 1981 – British television: on Coronation Street, Ken Barlow marries Deirdre Langton, which proves to be a national event scoring massive viewer numbers for the show.

Jinjur proves to be an incompetent ruler, but a female advocating gender equality is ultimately placed on the throne.

His mission is to get a single man out of the camp, but he has to improvise when his target proves to be on the verge of death.

The discovery of short runic inscriptions on a great number of articles for common personal use proves that the knowledge and use of the runic script was generally spread among the old Turkic tribes.

Owain is perhaps best remembered outside Wales as the mysterious Welshman of ' Owen Glendower ' in Shakespeare's Henry IV, Part 1 who claims to be able to " call spirits from the vasty deep ," and proves later on that he can, at least, summon unearthly music.

* The Mongols land on Java, taking the capital, but it proves impossible to hold.

* Galerius, Roman Caesar in the Balkan, proves his worth in campaigning on the Danube frontier, fighting the Goths, Marcomanni, Sarmatians, and Carpi.

The book introduces the concept of spherical triangle ( figures formed of three great circle arcs, which he named " trilaterals ") and proves Menelaus ' theorem on collinearity of points on the edges of a triangle ( which may have been previously known ) and its analog for spherical triangles.

The game starts with Kyle Katarn and Jan Ors investigating a supposedly abandoned Imperial outpost on Kejim, which proves to be crawling with Imperial forces.

Its first appearance is on a Constantinian silver coin from c. 317, which proves that Constantine did use the sign at that time, though not very prominently.

The mean value theorem proves that this must be true: The slope between any two points on the graph of f must equal the slope of one of the tangent lines of f. All of those slopes are zero, so any line from one point on the graph to another point will also have slope zero.

From the first moment of the marriage, Anne was under pressure to provide James and Scotland with an heir, but the passing of 1591 and 1592 with no sign of a pregnancy provoked renewed Presbyterian libels on the theme of James ’ s fondness for male company and whispers against Anne " for that she proves not with child.

The 2011 Martin Scorsese film Hugo initially focuses on a mysterious notebook taken from the main character and his struggle to retrieve it ; " The notebook, of course, is just another storytelling device ( the McGuffin ) that ultimately proves irrelevant.

At the trial, he reveals his true identity and proves it by showing the convict brand on his chest.

Assuming p, one proves R and ¬ R, and concludes from this that p → ( R ∧ ¬ R ).

Assuming ¬ p, one proves R and ¬ R, and concludes from this that ¬ p → ( R ∧ ¬ R ).

But any multiple in of has leading term divisible by q and constant term divisible by p, which proves the statement.

In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true ,< ref > The word " true " is used disquotationally here: the Gödel sentence is true in this sense because it " asserts its own unprovability and it is indeed unprovable " ( Smoryński 1977 p. 825 ; also see Franzén 2005 pp. 28 – 33 ).

It is also possible to read " G < sub > T </ sub > is true " in the formal sense that primitive recursive arithmetic proves the implication Con ( T )→ G < sub > T </ sub >, where Con ( T ) is a canonical sentence asserting the consistency of T ( Smoryński 1977 p. 840, Kikuchi and Tanaka 1994 p. 403 )</ ref > but not provable in the theory ( Kleene 1967, p. 250 ).

Applying both sides to e < sub > j </ sub >, the result on each side is the jth partial derivative of f at p. Since p and j were arbitrary, this proves the formula (*).

For example instead of showing directly p ⇒ q, one proves its contrapositive ~ q ⇒ ~ p ( one assumes ~ q and shows that it leads to ~ p ).

the inverse function theorem proves that F < sup >-1 </ sup > has a total derivative at p.

If either p < sub > n </ sub ># + 1 or p < sub > n </ sub ># − 1 is a primorial prime, it means that there are larger primes than the nth prime ( if neither is a prime, that also proves the infinitude of primes, but less directly ; note that each of these two numbers has a remainder of either p − 1 or 1 when divided by any of the first n primes, and hence cannot be a multiple of any of them ).

By class field theory, this can only be true if there is an unramified extension of the field of pth roots of unity by a cyclic extension of degree p which behaves in the specified way under the action of Σ ; Ribet proves this by actually constructing such an extension using methods in the theory of modular forms.

* CMJ ( 10 / 16 / 00, p. 28 )-" slick and styled funk proves light years ahead of his peers.

However, as showed, a polynomial identity that provides a solution for values of n congruent to r mod p can exist only when r is not a quadratic residue modulo p. For instance, 2 is a not a quadratic residue modulo 3, so the existence of an identity for values of n that are congruent to 2 modulo 3 does not contradict Mordell's result, but 1 is a quadratic residue modulo 3 so the result proves that there can be no similar identity for values of n that are congruent to 1 modulo 3.

The knowledge in virtue of which a man is an historian is a knowledge of what the evidence at his disposal proves about certain events ''.

If we go all gooey over this newest Castro ( until he proves he isn't ) we've got rocks in our heads.

The Suez-Hungary crisis proves that this system was not invented by the new Administration, but only made more consistent and more active.

I have heard people talk with contempt about the British regulars, but that only proves that a lot of people talk about things of which they are deplorably ignorant.

What Sam Rayburn's life proves to us all is the magnificent lesson in political science that one can devotedly and with absolute dedication represent the seemingly provincial interests of one's own community, one's own district, one's own State, and by that help himself represent even better the sweep and scope of the problems of this the greatest nation of all time.

It can then grow steadily as it proves itself and as the need for it is demonstrated.

One could also add to these analogies that steel loses its magnetism by heat, which proves that steel becomes a better conductor through a rise in temperature, just as electrical bodies do.

Perhaps a course in typewriting might be regarded as the exception which proves the rule.

We have not the leisure, or the patience, or the skill, to comprehend what was working in the mind and heart of a then recent graduate from the Harvard Divinity School who would muster the audacity to contradict his most formidable instructor, the majesterial Andrews Norton, by saying that, while he believed Jesus `` like other religious teachers '', worked miracles, `` I see not how a miracle proves a doctrine ''.

But we would like your permission to do -- that is, to go further if it proves necessary ''.

The story indicates that Epimenides was probably heir to the shamanic religions of Asia, and proves together with the Homeric hymn, that Crete had a resisting religion up to the historical times.

A few days after the sermon, Paneloux is taken ill. His symptoms do not conform to those of the plague, but the disease still proves fatal.

In chapter 21 of The Murder of Roger Ackroyd, for example, Poirot talks about a mentally disabled nephew: this proves to be a ruse so that he can find out about homes for the mentally unfit, and in Dumb Witness, Poirot tells of an elderly invalid mother as a pretence to investigate the local nurses.

The same argument proves that no subfield of the real field is algebraically closed ; in particular, the field of rational numbers is not algebraically closed.

However, Odysseus proves to be more eloquent, and the council gives him the armor.

This proves the desired upper bound.

An inscription confirms the struggle between the native Egyptian and the foreign soldiery, and proves that Apries was killed and honourably buried in the third year of Amasis ( c. 567 B. C. E .).