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.

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.

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.

Certain government bureaucracies, such as a department of motor vehicles will issue an abstract of a completed transaction or an updated record intended to serve as a proof of compliance with some administrative requirement.

Chaitin prefaces his definition with: " I'll show you can't prove that a program is ' elegant '"— such a proof would solve the Halting problem ( ibid ).

He had introduced the adele ring in the late 1930s, following Claude Chevalley's lead with the ideles, and given a proof of the Riemann – Roch theorem with them ( a version appeared in his Basic Number Theory in 1967 ).

* Metamath-a language for developing strictly formalized mathematical definitions and proofs accompanied by a proof checker for this language and a growing database of thousands of proved theorems ; while the Metamath language is not accompanied with an automated theorem prover, it can be regarded as important because the formal language behind it allows development of such a software ; as of March, 2012, there is no " widely " known such software, so it is not a subject of " automated theorem proving " ( it can become such a subject ), but it is a proof assistant.

He had been well educated, and was versed in grammar and rhetoric, and had already, while still a young man, and before reaching the episcopate, given proof to those who dwelt with him of his wisdom and acumen " ( Soz., II, xvii ).

* California Penal Code Section 159: " No person can be convicted of common barratry except upon proof that he has excited suits or proceedings at law in at least three instances, and with a corrupt or malicious intent to vex and annoy.

From his own captains, Nelson was presented with a sword and a portrait as " proof of their esteem ".

Once again, however, there is a lack of archaeological proof for this reconstruction, and the sheer number of brochs, sometimes in places with a lack of good land, makes it problematic.

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 ).

In these memoirs, he paints himself as a born comedian, careless, light-hearted and with a happy temperament, proof against all strokes of fate, yet thoroughly respectable and honorable.

One proof of the chain rule begins with the definition of the derivative:

In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

* 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 ")

An objection against the theist implication of the proposition is that even if one accepts the argument as a proof of a First Cause, it does not identify that First Cause with God.

Modern bolts are stamped with a proof mark to ensure their consistent weight.

While this aspect is similar to Scotch and Irish whisky regulations, it contrasts with the maximum alcoholic proof limits on distillation ( 80 % abv ) and aging ( 62. 5 % abv ) purity allowed in the production of straight whiskey in the U. S. All spirits used in making a Canadian whisky must be aged for at least three years in wooden barrels of not greater than 700 L capacity ( a requirement similar to that for Scotch and Irish whisky and longer than for American straight whisky ).

However, in January 2011, the Spanish government denied a request by the U. S. ambassador to return the painting to the Cassirer family in California, which claims with proof that it was among those illegally taken by Nazis in Germany.

( For groups of low 2-rank the proof of this breaks down, because theorems such as the signalizer functor theorem only work for groups with elementary abelian subgroups of rank at least 3.

In this reality, the only proof that Charles Xavier ever existed is a secret monument in Magneto's palace garden, with the engraved message " He died so Genosha could live ".

Hubbard claimed, in an interview with the New York Times in November 1950, that " he had already submitted proof of claims made in the book to a number of scientists and associations.

Irenaeus pointed to Scripture as a proof of orthodox Christianity against heresies, classifying as Scripture not only the Old Testament but most of the books now known as the New Testament, while excluding many works, a large number by Gnostics, that flourished in the 2nd century and claimed scriptural authority.

" The IACHR also stated that: " The Commission is of the view that the new regime did not have, and does not now have, a policy of violating the right to life of political enemies, including among the latter the former guardsmen of the Government of General Somoza, whom a large sector of the population of Nicaragua held responsible for serious human rights violations during the former regime ; proof of the foregoing is the abolition of the death penalty and the high number of former guardsmen who were prisoners and brought to trial for crimes that constituted violations of human rights.

Depending on the value of n, we specify a sufficiently large positive integer k ( to meet our needs later ), and multiply both sides of the above equation by, where the notation will be used in this proof as shorthand for the integral:

Here, we present a common simple proof limited to the approximation of two antennas separated by a large distance compared to the size of the antenna, in a homogeneous medium.

The fundamental property of used in the proof above is that there cannot be a chain of positive integers where each integer in the chain is strictly less than its predecessor ; in other words, the ring of integers is not " too large " since it cannot sustain such a " large chain ".

It is characteristic of Cranach's prolific output, and a proof that he used a large workshop, that he received payment at Wittenberg in 1533 for " sixty pairs of portraits of the elector and his brother " on one day.

Allegations of predatory pricing by large companies can be the basis for a monopolization claim, but it is difficult to establish the required elements of proof.

Vinogradov's original proof, as it used the ineffective Siegel – Walfisz theorem, did not give a bound for " sufficiently large "; his student K. Borozdin proved, in 1939, that 3 < sup > 14348907 </ sup > is large enough.

Ol ' shanskii found some striking counterexamples for sufficiently large odd exponents ( greater than 10 < sup > 10 </ sup >), and supplied a considerably simpler proof based on geometric ideas.

Secondly, while Ramsey theory results do say that sufficiently large objects must necessarily contain a given structure, often the proof of these results requires these objects to be enormously large – bounds that grow exponentially, or even as fast as the Ackermann function are not uncommon.

The large prime database of The Prime Pages website records the top 20 primes of various special forms ; one of them is proof of primality using the elliptic curve primality proving ( ECPP ) algorithm.

It went through a series of crisis with paradoxical results, until the discoveries stabilized during the 20th century as a large and coherent body of mathematical knowledge with several aspects or components ( set theory, model theory, proof theory ...), whose detailed properties and possible variants are still an active research field.

Amongst his most original contributions were: his " Conjecture II " ( still open ) on Galois cohomology ; his use of group actions on Trees ( with H. Bass ); the Borel-Serre compactification ; results on the number of points of curves over finite fields ; Galois representations in ℓ-adic cohomology and the proof that these representations have often a " large " image ; the concept of p-adic modular form ; and the Serre conjecture ( now a theorem ) on mod-p representations that made Fermat's last theorem a connected part of mainstream arithmetic geometry.

* The midrash of several younger tannaim and of a large number of amoraim who did not interpret a Biblical passage as an actual proof of the halakha, but merely as a suggestion or a support for it (" zekher le-davar "; " asmakhta ").

This book provides a good introduction and summary of the proof, with a large section dedicated to Gödel's numbering.

So unlike the previous case of x and 2x we don't get a proof of Legendre's conjecture even for all large n. Error estimates on the PNT are not ( indeed, cannot be ) sufficient to prove the existence of even one prime in this interval.

When the fort was abandoned in September 1863, the CSA forces left behind a large amount of gunpowder in the bomb proof.

The gist of the following elementary proof is due to Paul Erd &# 337 ; s. The basic idea of the proof is to show that a certain central binomial coefficient needs to have a prime factor within the desired interval in order to be large enough.

* Use of computer programs to check a large but finite number of cases to complete a computer-assisted proof by exhaustion

In 1838, he spoke to over 5000 " working class men " in Manchester and told them that the presence of so large an audience gave him the proof that " the working class man was with him ".

The concept of child sacrifice via burning them or placing them within a heated bronze statue of the god comes from Greek accounts and is not historically verifiable as no archaeological proof of such a large, bronze statue exists.