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.

Also, reserve the right to demand proof of death despite the fact that you'll probably never use it.

Euclid stipulated this so that he could construct a reductio ad absurdum proof that the two numbers ' common measure is in fact the greatest.

In fact, Zermelo initially introduced the axiom of choice in order to formalize his proof of the well-ordering theorem.

This observation, and the fact that kill timeframes shorten as the percentage of copper in an alloy increases, is proof that copper is the ingredient in brass and other copper alloys that kills the microbes.

An " elementary " proof can be given using the fact that geometric mean of positive numbers is less than arithmetic mean

The proof for the fact that no co-NP-complete problem can be in NP, if NP is unequal co-NP, is symmetrical.

Noting another proof that self-replicating machines are possible is the simple fact that all living organisms are self replicating by definition.

It is particularly commonly employed in issues of law where proof of guilt or innocence may be required, or when it must be determined whether a person knew a particular fact before taking a specific action ( e. g., whether an action was premeditated ).

In fact, the same proof shows that Euler's formula is even valid for all complex numbers z.

In fact, Cantor's method of proof of this theorem implies the existence of an " infinity of infinities ".

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.

#* 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 >

Other criticism concerning outing centers upon the harm that outing individuals as homosexual, transgender, or transsexual does to them personally and professionally and upon the fact that some individuals have been erroneously outed or have been outed when there is no proof to substantiate the claim that they are gay, transgendered, or transsexual.

Only by the strongest pressure of the Crown were Parliaments maintained during the first century of their existence and the best proof of this assertion lies in the fact that in those countries where the Crown was weak, Parliament ceased to exist.

It placed subjects in a situation where an accusation of academic fraud ( cheating ) could be made, of which some subjects were in fact by design actually guilty ( and knew this ), and some were innocent but faced seemingly strong evidence of guilt and no verifiable proof of innocence.

To rigorously complete the proof there are still serious technicalities to overcome, due to the fact that the summation over zeta zeros in the explicit formula for does not converge absolutely but only conditionally and in a " principal value " sense.

In fact, it follows from the proof of Hadamard and de la Vallée Poussin that

Although little is known about this period in Rome, there is one thing that is for certain: the fact that Boniface ’ s last reign lasted eleven months without any imperial intervention is evidence of not only the weakness of the government of this time, but also is proof that despite his actions and opposition, he must have had much support.

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.

Again, a rigorous proof is needed for the fact that does not admit an equivalent regular expression of lower star height.

Saddam routinely cited his survival as " proof " that Iraq had in fact won the war against the U. S. This message earned Saddam a great deal of popularity in many sectors of the Arab world.

Despite the fact that there has never been proof that Wharton's Hellfire Club ever did more than hold mock religious ceremonies and drink excessively, Wharton's political opposition used his membership as a way to pit him against his political allies, thus removing him from parliament.

Evans's argument appears to show that there can be no vague identities ( e. g. " Princeton = Princeton Borough "), but as Lewis ( 1988 ) makes clear, Evans takes for granted that there are in fact vague identities, and that any proof to the contrary cannot be right.

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

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.

The proof relies on the Pythagorean theorem.

The proof relies on the assumption that mass is constant ; this is valid only in non-relativistic systems in which no mass is being ejected.

Since the proof Evans produces relies on the assumption that terms precisely denote vague objects, the implication is that the assumption is false, and so the vague-objects view is wrong.

For example, Euclid provides an elaborate proof of the Pythagorean theorem, by using addition of areas instead of the much simpler proof from similar triangles, which relies on ratios of line segments.

The proof of the global embedding theorem relies on Nash's far-reaching generalization of the implicit function theorem, the Nash – Moser theorem and Newton's method with postconditioning.

A theorem of Lackenby and Meyerhoff, whose proof relies on the geometrization conjecture and computer assistance, holds that 10 is the largest possible number of exceptional surgeries of any hyperbolic knot.

However, in England and Wales, the Magistrates ' Courts Act 1980, s. 101 stipulates that where a defendant relies on some " exception, exemption, proviso, excuse or qualification " in his defence, the legal burden of proof as to that exception falls on the defendant, though only on the balance of probabilities.

Wantzel's proof relies on ideas from the field of Galois theory — in particular, trisection of an angle corresponds to the solution of a certain cubic equation, which is not possible using the given tools.

As a result of surface area minimization, a surface will assume the smoothest shape it can ( mathematical proof that " smooth " shapes minimize surface area relies on use of the Euler – Lagrange equation ).

The proof that A < sub > T </ sub > is closed under addition relies on the commutativity of addition ( see examples section ).

Whether one is estimating the total cost of their groceries, calculating miles per gallon, or figuring out how many minutes on the treadmill that chocolate éclair will require, math as used by most people relies less on proof than on practicality ( i. e., does it answer the question?

Gauss's proof relies firstly on the fact that constructibility is equivalent to expressibility of the trigonometric functions of the common angle in terms of arithmetic operations and square root extractions, and secondly on his proof that this can be done if the odd prime factors of n are distinct Fermat primes, which are of the form.

This proof relies on the chain rule and on the properties of the natural logarithm function, both of which are deeper than the product rule.

The proof most commonly seen in textbooks relies on the contraction mapping principle, also known as the Banach fixed point theorem.

In mathematics, a proof by infinite descent is a particular kind of proof by contradiction which relies on the facts that the natural numbers are well ordered and that there are only a finite number of them that are smaller than any given one.

Nearly every proof which explicitly relies on the axiom of choice is non-constructive in nature because this axiom is fundamentally non-constructive.

This proof is non-constructive because it relies on the statement " Either q is rational or it is irrational "— an instance of the law of excluded middle, which is not valid within a constructive proof.

In general, if a protocol is proven secure, attacks to that protocol must break one of the assumptions in the proof ; for instance if the proof relies on the hardness of integer factorization, to break this assumption one must discover a fast integer factorization algorithm.