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 ).

Euclid often used proof by contradiction.

Later ancient commentators such as Proclus ( 410 – 485 CE ) treated many questions about infinity as issues demanding proof and, e. g., Proclus claimed to prove the infinite divisibility of a line, based on a proof by contradiction in which he considered the cases of even and odd numbers of points constituting it.

Euclid frequently used the method of proof by contradiction, and therefore the traditional presentation of Euclidean geometry assumes classical logic, in which every proposition is either true or false, i. e., for any proposition P, the proposition " P or not P " is automatically true.

Such a model ( precisely, the set of " natural numbers " it contains ) is necessarily non-standard, as it contains the code number of a proof of a contradiction of T.

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.

#* Note: This fact provides a proof of the infinitude of primes distinct from Euclid's Theorem: if there were finitely many primes, with p being the largest, we reach an immediate contradiction since all primes dividing 2 < sup > p </ sup > − 1 must be larger than p .</ li >

In logic, proof by contradiction is a form of proof that establishes the truth or validity of a proposition by showing that the proposition's being false would imply a contradiction.

Proof by contradiction is also known as indirect proof, apagogical argument, proof by assuming the opposite, and reductio ad impossibilem.

A classic proof by contradiction from mathematics is the proof that the square root of 2 is irrational.

The method of proof by contradiction has also been used to show that for any non-degenerate right triangle, the length of the hypotenuse is less than the sum of the lengths of the two remaining sides.

In mathematical logic, the proof by contradiction is represented as:

Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum also known as proof by contradiction.

These cases demonstrate a paradox not in the sense that they demonstrate a logical contradiction, but in the sense that they demonstrate a counter-intuitive result that is provably true: the situations " there is a guest to every room " and " no more guests can be accommodated " are not equivalent when there are infinitely many rooms ( an analogous situation is presented in Cantor's diagonal proof ).

A proof of uniqueness by contradiction is as follows.

# Then used resolution to attempt to obtain a proof by contradiction by adding the clausal form of the negation of the theorem to be proved.

Also, using proof by contradiction is problematical because the axiomatizations of all practical domains of knowledge are inconsistent in practice.

In addition, some adherents of these schools reject non-constructive proofs, such as a proof by contradiction.

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.

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 ".

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:

If we insert vertices in random order, it turns out ( by a somewhat intricate proof ) that each insertion will flip, on average, only O ( 1 ) triangles – although sometimes it will flip many more.

If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.

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.

Lessing outlined the concept of the religious " Proof of Power ": How can miracles continue to be used as a base for Christianity when we have no proof of miracles?

Any of the several well-known axiomatisations will do ; we assume without proof all the basic well-known results about our formalism ( such as the normal form theorem or the soundness theorem ) that we need.

We approach the proof of Theorem 2 by successively restricting the class of all formulas φ for which we need to prove " φ is either refutable or satisfiable ".

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:

This is why we cannot naively use the argument appearing at the comment which precedes the proof.

" Following in the June 1816 Eclectic Review, Josiah Conder dismissed the poem: " As to ' Kubla Khan ', and the ' Pains of Sleep ', we can only regret the publication of them, as affording a proof that the Author over-rates the importance of his name.

If a statement P is provable, then it is certainly impossible to prove that there is no proof of P. But even if it can be shown that no disproof of P is possible, we cannot conclude from this absence that there is a proof of P. Thus P is a stronger statement than not-not-P.

The proof works just as well if we have an algorithm for deciding any other nontrivial property of programs, and will be given in general below.

Finally, we provide a proof of the related result, rk ( A ) =

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:

In like manner, I apprehend, the sole evidence it is possible to produce that anything is desirable, is that people do actually desire it … No reason can be given why the general happiness is desirable, except that each person, so far as he believes it to be attainable, desires his own happiness … we have not only all the proof which the case admits of, but all which it is possible to require, that happiness is a good: that each person's happiness is a good to that person, and the general happiness, therefore, a good to the aggregate of all persons .”

* How do we know whether a mathematical proof is correct?

Who then is likely to listen, let alone to respond, to the proof that nothing short of major movements of population can shift the lines along which we are being carried towards disaster?

When he gets close to us, we can confirm ( verify ) that he is Socrates and not Theaetetus through the proof of our eyesight.

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.