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.

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.

so that the absence of the hymen is by no means positive proof that a girl has had sex relations.

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.

Narayanan – AIR India Reporter 1988 Court Page No. 1381 ; 1988 Volume No. 3 SCC Court Cases Page No. 366 ; 1988 PLJR 78 – Although an affidavit may be taken as proof of the facts stated therein, the Courts have no jurisdiction to admit evidence by way of affidavit.

The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem.

Because of independence, the decision whether to use of the axiom of choice ( or its negation ) in a proof cannot be made by appeal to other axioms of set theory.

That was so because it not only was proof of excessive pride, but also resulted in violent acts by or to those involved.

The terms ' integrative ' or ' integrated medicine ' indicate combinations of conventional and alternative medical treatments that have some scientific proof of efficacy ; such practices are viewed by advocates as the best examples of complementary medicine.

Mordell's theorem had an ad hoc proof ; Weil began the separation of the infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology, which was not to be clearly named as that for two more decades.

This key result opened the way for a proof of the Weil conjectures, ultimately completed by his student Pierre Deligne.

Canova in 1817 by George Hayter ( British Embassy, Paris ) There was, however, another proof, which modesty forbade him to mention, an ever-active benevolence, especially towards artists.

However, there have been many wild claims of ancient mid eastern ancestry ( including Assyrian ) throughout Europe, Africa and even the Americas, none of which have been supported by mainstream opinion or strong evidence, let alone proof.

Stilicho is alleged by some to have wanted control of both Emperors, and is supposed to have had Rufinus assassinated by Gothic mercenaries in 395 ; though definite proof of Stilicho's involvement in the assassination is lacking, the intense competition and political jealousies engendered by the two figures compose the main thread of the first part of Arcadius ' reign.

* 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.

A FAT usually includes a check of completeness, a verification against contractual requirements, a proof of functuality ( either by simulation or a conventional function test ) and a final inspection.

This is not a rejection of existence by Gilson, a leading modern metaphysician in the classical tradition: " philosophers are wholly justified in taking existence for granted ... and in never mentioning it again ...." In Gilson's view, the participial being is a given, a primitive of experience, not subject to proof or investigation, as it is the grounds of proof.

The first proof was given by (), where the formulation of the problem was attributed to Ulam.

SAT was the first known NP-complete problem, as proved by Stephen Cook in 1971 ( see Cook's theorem for the proof ).

Although there is no definite proof of the date of his birth, it has been suggested by Ukrainian historian Mykhaylo Maksymovych that it is likely 27 December 1595 ( St. Theodore's day ).

( A formal proof for all finite sets would use the principle of mathematical induction to prove " for every natural number k, every family of k nonempty sets has a choice function.

The proof of the independence result also shows that a wide class of mathematical statements, including all statements that can be phrased in the language of Peano arithmetic, are provable in ZF if and only if they are provable in ZFC.

We can call a person, a house, a symphony, a fragrance, and a mathematical proof beautiful.

A more general binomial theorem and the so-called " Pascal's triangle " were known in the 10th-century A. D. to Indian mathematician Halayudha and Persian mathematician Al-Karaji, in the 11th century to Persian poet and mathematician Omar Khayyam, and in the 13th century to Chinese mathematician Yang Hui, who all derived similar results .< ref > Al-Karaji also provided a mathematical proof of both the binomial theorem and Pascal's triangle, using mathematical induction.

For the proof of the equivalence of the four approaches the reader is referred to mathematical expositions like or.

Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.

The Clay Mathematics Institute has offered a $ 1 million USD prize for the first correct proof, along with prizes for six other mathematical problems.

The study of mathematical proof is particularly important in logic, and has applications to automated theorem proving and formal verification of software.

In this way we get a proof of the Euler – Maclaurin summation formula by mathematical induction, in which the induction step relies on integration by parts and on the identities for periodic Bernoulli functions.

As for other popular public key cryptosystems, no mathematical proof of security has been published for ECC.

The prevailing opinion at the time was that one should first write a program and then provide a mathematical proof of correctness.

Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics.

The version given below attempts to represent all the steps in the proof and all the important ideas faithfully, while restating the proof in the modern language of mathematical logic.

Hilbert produced an innovative proof by contradiction using mathematical induction ; his method does not give an algorithm to produce the finitely many basis polynomials for a given ideal: it only shows that they must exist.

Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers ( positive integers ).

The earliest implicit traces of mathematical induction can be found in Euclid's proof that the number of primes is infinite and in Bhaskara's " cyclic method ".

An implicit proof by mathematical induction for arithmetic sequences was introduced in the al-Fakhri written by al-Karaji around 1000 AD, who used it to prove the binomial theorem and properties of Pascal's triangle.

The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.

The first example of this is a mathematical proof of the confinement mechanisms in EROS, based on a simplified model of the EROS API.

In the case of seL4, complete formal verification of the implementation has been achieved, i. e. a mathematical proof that the kernel's implementation is consistent with its formal specification.

Thus the proof of the existence of a mathematical object is tied to the possibility of its construction.