The Elements of Theology, which consists of 211 propositions, each followed by a proof, beginning from the existence of the One ( the first principle of all things ) and ending with the descent of individual souls into the material world.

The difference is that instead of constructing a new proof, the proof verifier simply checks that a provided formal proof ( or, in instructions that can be followed to create a formal proof ) is correct.

He may well have died in the late 160s, as a result of the Antonine Plague that followed the Parthian War, though conclusive proof is lacking.

Little's proof was followed by a simpler version by Jewell and another by Eilon.

** Mitchell Feigenbaum's discovery of the Feigenbaum constant was based initially on numerical observations, followed by a rigorous proof.

Mounting complaints by 9-5 owners forced GM to offer an eight-year warranty on the engine in 4-cylinder models for original owners, provided the owner can produce proof that they followed the manufacturer's oil change intervals.

Leonte Landino, a baseball journalist and researcher for the Society of American Baseball Research ( SABR ) followed the path of longtime baseball writer Juan Vene and led the investigation along with Nick Martinez, a baseball researcher in Nevada about Castro's life and proof of birth outside the United States.

The logical structure of the Disquisitiones ( theorem statement followed by proof, followed by corollaries ) set a standard for later texts.

This conjecture of Ramanujan followed from the proof of the Weil conjectures by.

The removal of the censure followed ( 1781 ) when Hontheim published at Frankfort what purported to be a proof that his submission had been made of his own free will ( Justini Febronii acti commentarius in suam retractationem, etc .).

If the decisions were favourable, the general meeting of the congregation was followed by a decree, confirmed by the pope, in which it was announced that there was proof of miracles.

By a decree of 21 January 2009 ( Protocol Number 126 / 2009 ), which was issued in response to a renewed request that Bishop Fellay made on behalf of all four bishops whom Lefebvre had consecrated on 30 June 1988, the Prefect of the Congregation for Bishops, by the power expressly granted to him by Pope Benedict XVI, remitted the automatic excommunication that they had thereby incurred, and expressed the wish that this would be followed speedily by full communion of the whole of the Society of Saint Pius X with the Church, thus bearing witness, by the proof of visible unity, to true loyalty and true recognition of the Pope's Magisterium and authority.

Although the commission found no proof for these allegations, the provincial Conservatives won the general election that followed two years later.

Strabo ascribes its foundation to a body of Pylians, a part of those who had followed Nestor to Troy ; while Justin tells us it was founded by Epeius, the hero who constructed the wooden horse at Troy ; in proof of which the inhabitants showed, in a temple of Minerva, the tools used by him on that occasion.

A credulousness, a distaste for documentation, an uncritical reliance on contemporary accounts, and a proneness to assume a theory as true before adequate proof was provided were all evidences of his failure to comprehend the use of the scientific method or to evaluate the responsibilities of the historian to his reading public.

The first is the strictly scientific, which demands concrete proof and therefore may err on the conservative side by waiting for evidence in the flesh.

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.

Since the change to better nutrition, he feels he can report on improvements in health, though he considers the following statements observations and not scientific proof.

Most of them, the world over, operate on the same principle by which justice is administered in France and some other Latin countries: the customer is to be considered guilty of abysmal ignorance until proven otherwise, with the burden of proof on the customer himself.

At some point, he was alleged to have accompanied Swein on a pilgrimage to the Holy Land, but proof is lacking.

* Natarajan Shankar SRI International, work on decision procedures, little engines of proof, co-developer of PVS.

Following Desargues ' thinking, the sixteen-year-old Pascal produced, as a means of proof, a short treatise on what was called the " Mystic Hexagram ", Essai pour les coniques (" Essay on Conics ") and sent it — his first serious work of mathematics — to Père Mersenne in Paris ; it is known still today as Pascal's theorem.

where the rule is that wherever instances of "" and "" appear on lines of a proof, "" can validly be placed on a subsequent line.

where the rule is that wherever an instance of "" appears on a line of a proof, either "" or "" can be placed on a subsequent line ;

Although there is no proof, the name " Thomas Corbett " does appear on the list of dead and missing.

The burden of proof should be on the people who make these statements, to show where they got their information from, to see if their conclusions and interpretations are valid, and if they have left anything out.

An inscription on a stone built into the wall of a summer house in Lancarffe furnishes proof of a settlement in Bodmin in the early Middle Ages.

He / she must have a valid passport and either have an invitation letter or a bank statement with enough money to survive the length of the stay in Costa Rica, plus proof of onward travel ( ticket to exit Costa Rica & legal ability to travel to the destination stated on the ticket ).

Maimonides argued that executing a defendant on anything less than absolute certainty would lead to a slippery slope of decreasing burdens of proof, until we would be convicting merely " according to the judge's caprice ".

Bolzano's proof relied on the method of bisection: the sequence was placed into an interval that was then divided into two equal parts, and a part containing infinitely many terms of the sequence was selected.

# Every net on X has a convergent subnet ( see the article on nets for a proof ).

The first proof relies on a theorem about products of limits to show that the derivative exists.

* 1799: Doctoral dissertation on the Fundamental theorem of algebra, with the title: Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (" New proof of the theorem that every integral algebraic function of one variable can be resolved into real factors ( i. e., polynomials ) of the first or second degree ")

In anticipation of its eventual proof, some have proceeded to develop further proofs which are contingent on the truth of this conjecture.

Whether you experienced the passion of desire I have, of course, no way of knowing, nor indeed have I wished with even the most fleeting fragment of a wish to know, for the fact that one constitutes by one's mere existence so to speak the proof of some sort of passion makes any speculation upon this part of one's parents' experience more immodest, more scandalizing, more deeply unwelcome than an obscenity from a stranger.

Both Alfred Harcourt and Donald Brace had written him enthusiastic praise of Elmer Gantry ( any changes could be made in proof, which was already coming from the printer ) and they had ordered 140,000 copies -- the largest first printing of any book in history.

It is possible, however, that there is a shorter proof of a theorem from ZFC than from ZF.

Among his major accomplishments were the 1940 proof, of the Riemann hypothesis for zeta-functions of curves over finite fields, and his subsequent laying of proper foundations for algebraic geometry to support that result ( from 1942 to 1946, most intensively ).

Paul Beekman Taylor used the Ynglingasaga as proof that the Beowulf poet was likewise working from Germanic tradition.

In the course of the proof, he made use of a lemma that from any countable cover of the interval by smaller open intervals, it was possible to select a finite number of these that also covered it.

Eventually, complete proof came from chromosome maps in Morgan's own lab.

As an example of a conditional proof in symbolic logic, suppose we want to prove A → C ( if A, then C ) from the first two premises below:

More recently, both Elms and librarian Lee Weinstein have gathered circumstantial evidence to support the case for Linebarger's being " Allen ," but both concede there is no direct proof that Linebarger was ever a patient of Lindner's or that he suffered from a disorder similar to that of " Kirk Allen.

The rule makes it possible to eliminate a disjunction from a logical proof.

At the last moment, when his immense work was drawing to an end, he encountered a crowning mortification: he discovered that the bookseller, fearing the government's displeasure, had struck out from the proof sheets, after they had left Diderot's hands, all passages that he considered too dangerous.

In propositional logic, disjunction elimination ( sometimes named proof by cases or case analysis ), is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.

A proof from Euclid's elements that, given a line segment, an equilateral triangle exists that includes the segment as one of its sides.

* Axiomatic proof: Proofs are deductive derivations of propositions from primitive premises that are ‘ true ’ in some sense.

* Analytic proof: Proofs are non-deductive derivations of hypotheses from problems.

The imaginary company had produced a proof of the Riemann Hypothesis but then had great difficulties collecting royalties from mathematicians who had proved results assuming the Riemann Hypothesis.

* Fermat's Last Theorem Blog: Unique Factorization, A blog that covers the history of Fermat's Last Theorem from Diophantus of Alexandria to the proof by Andrew Wiles.

He asked Cantor to withdraw the paper from Acta while it was in proof, writing that it was "... about one hundred years too soon.

It is deduced from the model existence theorem as follows: if there is no formal proof of a formula then adding its negation to the axioms gives a consisten theory, which has thus a model, so that the formula is not a semantic consequence of the initial theory.

Despite multiple parliamentary questions from as early as 2005, where it was stated that there was no proof that this was happening, Minister Ahern announced a ban on all handguns in November 2008.

The following lemma, which Gödel adapted from Skolem's proof of the Löwenheim-Skolem theorem, lets us sharply reduce the complexity of the generic formula for which we need to prove the theorem:

He tied this interest into his racist philosophy, looking for proof of Aryan and Nordic racial superiority from ancient times.