Cantor's work is of great philosophical interest, a fact of which he was well aware.

And in fact, Cantor's diagonal argument is constructive, in the sense that given a bijection between the real numbers and natural numbers, one constructs a real number which doesn't fit, and thereby proves a contradiction.

This fact is a direct consequence of Cantor's theorem on the cardinality of the power set of a set.

The very fact that they came so near to winning by the wrong method, war, led directly to their losing both the war and the wrong thing they fought for, since it forced Lincoln to free their slaves as a military measure.

Following observation of the fact that the reaction rates of supposedly identical reaction mixtures prepared on the same filling manifold and exposed under identical conditions often differed by several hundred per cent, a systematic series of experiments was undertaken to see whether the difficulty could be ascribed to the method of preparing the chlorine, to the effects of oxygen or moisture or to the effect of surface to volume ratio in the reaction tubes.

In the indirect method, this was evident from the fact that tumor sections were stained light green even when stained with NS and Af or with Af only.

The fact that they use an impact printing method allows them to be used to print multi-part documents using carbonless copy paper, like sales invoices and credit card receipts, whereas other printing methods are unusable with paper of this type.

In the case of doubling the cube, the impossibility of the construction originates from the fact that the compass and straightedge method involve first-and second-order equations, while doubling a cube requires the solution of a third-order equation.

This method has several problems such as the fact that it cannot be used to score adults.

His laboratory notebooks, now in the Bibliothèque Nationale in Paris, in fact show Pasteur used the method of rival Jean-Joseph-Henri Toussaint, a Toulouse veterinary surgeon, to create the anthrax vaccine.

The basis for determination of molecular weight according to the Staudinger method ( since replaced by the more general Mark-Houwink equation ) is the fact that relative viscosity of suspensions depends on volumetric proportion of solid particles.

) In fact, if this method is used, Newton inversion of the natural logarithm may conversely be used to calculate the exponential function efficiently.

In fact, the GI of potatoes can vary considerably depending on type ( such as red, russet, white, or Prince Edward ), origin ( where it was grown ), preparation methods ( i. e., cooking method, whether it is eaten hot or cold, whether it is mashed or cubed or consumed whole, etc.

In fact, any method by which the atoms are directly and continuously excited from the ground state to the excited state ( such as optical absorption ) will eventually reach equilibrium with the de-exciting processes of spontaneous and stimulated emission.

Using the method often portrayed in movies and television of flipping the cylinder open and closed with a flick of the wrist can in fact cause the crane to bend over time, throwing the cylinder out of alignment with the barrel.

Combined with the fact that there is no single election system for the national presidential election and therefore no single method for IRV, there would be no way to guarantee that a national IRV election would save money – in fact it might cost even more.

In part this limitation arose from the fact that consciousness raising, as " the primary method of understanding women's condition " in the movement at this time and its " most successful organizing tool ", led to an emphasis on personal experience that concealed " prior political and philosophical assumptions ".

The other method just mentioned auscultation being rendered inadmissible by the age and sex of the patient, I happened to recollect a simple and well-known fact in acoustics,.

Nozick believed the counterfactual conditionals bring out an important aspect of our intuitive grasp of knowledge: For any given fact, the believer's method must reliably track the truth despite varying relevant conditions.

In fact Steinach ’ s method was doomed to failure because the immune system rejects transplanted glands, and was eventually exposed as ineffective and often harmful.

The Deutsch-Bobrow method of reference counting capitalizes on the fact that most reference count updates are in fact generated by references stored in local variables.

In his books, Time on the Cross and Without Consent or Contract: the Rise and Fall of American Slavery, Robert Fogel maintains that slavery was in fact a profitable method of production, especially on bigger plantations growing cotton that fetched high prices in the world market.

The historical significance of the Tantric method lies in the fact that it impacted every major Indian religion extant in the early medieval period ( c. 500-1200 CE ): thus the Hindu sects of Shaivism, Shaktism and Vaishnavism, as well as Buddhism and Jainism all developed a well-documented body of Tantric practices and related doctrines.

The value of the method lies in the fact that specific design problems, once encountered, are never seen again because they are immediately eliminated, while the parts that appear successful are tested over and over.

In 1837, Belgian botanist Charles François Antoine Morren discovered this fact and pioneered a method of artificially pollinating the plant.

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.

The proof of this fact relies on an algorithm which, given the first n digits of Ω, solves Turing's halting problem for programs of length up to n. Since the halting problem is undecidable, Ω can not be computed.

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.

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.