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 ).

The reader will find it helpful to think of the special case when the primes are of degree 1, and even more particularly, to think of the proof of Theorem 10, a special case of this theorem.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

For the frequent case of propositional logic, the problem is decidable but Co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.

In this case, if a proof uses this statement, researchers will often look for a new proof that doesn't require the hypothesis ( in the same way that it is desirable that statements in Euclidean geometry be proved using only the axioms of neutral geometry, i. e. no parallel postulate.

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 completed proof of the classification was announced by after Aschbacher and Smith published a 1221 page proof for the missing quasithin case.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

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.

Gödel's original proof of the theorem proceeded by reducing the problem to a special case for formulas in a certain syntactic form, and then handling this form with an ad hoc argument.

proved the theorem ( for the special case of polynomial rings over a field ) in the course of his proof of finite generation of rings of invariants.

The extension ψ is in general not uniquely specified by φ, and the proof gives no explicit method as to how to find ψ: in the case of an infinite dimensional space V, it depends on Zorn's lemma, one formulation of the axiom of choice.

However, there is a body of case law governing the civil commitment of individuals under the Fourteenth Amendment through U. S. Supreme Court rulings beginning with Addington v. Texas in 1979 which set the bar for involuntary commitment for treatment by raising the burden of proof required to commit persons from the usual civil burden of proof of " preponderance of the evidence " to the higher standard of " clear and convincing " evidence.

' In the second case, he cites an example that demonstrates ignorance of statistical principles in the lay press: ' Since no such proof is possible genetically modified food is harmless, the article in The New York Times was what is called a " bad rap " against the U. S. Department of Agriculture-a bad rap based on a junk-science belief that it's possible to prove a null hypothesis.

This might come in the form of a proof that the number in question is in fact irrational ( or rational, as the case may be ); or a finite algorithm that could determine whether the number is rational or not.

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.

It is widely believed that ( 1 ) is the case, although no proof as to the truth of either statement has yet been discovered.

In most legal proceedings, one party has a burden of proof, which requires it to present prima facie evidence for all of the essential facts in its case.

Rules of evidence govern whether, when, how, and for what purpose, proof of a legal case may be placed before a trier of fact for consideration.

Boehm claimed to have cured gay people in the fourth part of his series on homosexuality, but presented as proof a case in which “ the homosexuality never became conscious for the patient and had never expressed itself in manifest activity .” This patient does not appear to have been homosexual.

( 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.

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:

Nash's proof of the C < sup > k </ sup >- case was later extrapolated into the h-principle and Nash – Moser implicit function theorem.

The sequence F < sub > k </ sub > used in this proof corresponds to the Kleene chain in the proof of the Kleene fixed-point theorem.

The proof of the general case requires some commutative algebra, namely the fact, that the Krull dimension of k is one — see Krull's principal ideal theorem ).

The proof of subgraph isomorphism being NP-complete is simple and based on reduction of the clique problem, an NP-complete decision problem in which the input is a single graph G and a number k, and the question is whether G contains a complete subgraph with k vertices.

PP is not contained in SIZE ( n < sup > k </ sup >) for any k ( proof ).

An archetypal double counting proof is for the well known formula for the number of k-combinations ( i. e., subsets of size k ) of an n-element set:

The first proof, which is not combinatorial, uses mathematical induction and generating functions to find that the number of sequences of this type is ( 2 < sup > k </ sup > − 1 )< sup > n </ sup >.

The second proof is based on the observation that there are 2 < sup > k </ sup > − 1 proper subsets of the set

So || A < sup > k </ sup >||< sub >∞</ sub > is bounded for all k. This gives another proof that there are no eigenvalues which have greater absolute value than Perron-Frobenius one.

proved the conjecture for k = 6, also using the four color theorem ; their paper with this proof won the 1994 Fulkerson Prize.

The proof uses the fact that each Sq < sup > k </ sup > is decomposable for k which is not a power of 2 ;

* For small deflections, the tip-cantilever can be modeled as a damped harmonic oscillator with a proof mass ( m ) in, an ideal spring constant ( k ) in, and a damper ( D ) in.