However, as in Cantor's argument ( above ), this idea leads to difficulties.

However, in CL it is necessary to explicitly refer to the function namespace when passing a function as an argument — which is also a common occurrence, as in the example above.

" This form of the argument is far more difficult to separate from a purely first cause argument than is the example of the house's maintenance above, because here the First Cause is insufficient without the candle's or vessel's continued existence.

Given the definition of above, we might fix ( or ' bind ') the first argument, producing a function of type.

The above definition implies this one: the upper bound of the empty subset is any existing element of A, because A is nonempty ; furthermore, as provable with an induction argument over the size of nonempty finite subsets, the upper bound of a finite subset may be obtained by finding upper bounds of pairs iteratively.

Then, using the periodic Bernoulli function P < sub > n </ sub > defined above and repeating the argument on the interval, one can obtain an expression of ƒ ( 1 ).

In this notation, the use of a vertical bar as delimiter indicates that the argument following it is the " parameter " ( as defined above ), while the backslash indicates that it is the modular angle.

Heawood noticed Kempe's mistake and also observed that if one was satisfied with proving only five colors are needed, one could run through the above argument ( changing only that the minimal counterexample requires 6 colors ) and use Kempe chains in the degree 5 situation to prove the five color theorem.

The argument above may not hold for the universe as a whole, since travel times may well explain the lack of physical presence on Earth of alien inhabitants of far away galaxies.

An illustration of Cantor's diagonal argument for the existence of uncountable set s. The sequence at the bottom cannot occur anywhere in the infinite list of sequences above.

However, when k ≥ 3, the expected value is well-defined, and by the above argument, it is

Yet he attacks the idealism of Schopenhauer and Descartes with an argument similar to Kant's critique of the latter ( see above );

In the above argument, the assertion " this number is either rational or irrational " invokes the law of excluded middle.

In the argument above, for any and, whenever and are true, necessarily is true.

If S contains two elements that are not pairwise orthogonal ( in particular, the set of all quantum states includes such pairs ) then an argument like that given above shows that the answer is no.

Though some points above may be arguable, but some key points seemingly aren't giving that it would require one to abide by many of the premises to even make an argument to begin with.

In the Leipzig disputation with Martin Luther, 1519, Johann Eck used the Corpus, specifically the Angelic Hierarchy, as argument for the apostolic origin of papal supremacy, pressing the Platonist analogy, " as above, so below ".

Since E < sub > 2 </ sub >-E < sub > 1 </ sub > ≫ kT, it follows that the argument of the exponential in the equation above is a large negative number, and as such N < sub > 2 </ sub >/ N < sub > 1 </ sub > is vanishingly small ; i. e., there are almost no atoms in the excited state.

Paedobaptists point to a number of passages in the New Testament which seem to corroborate the above argument.

( In the above symbolic argument, " x is the smallest rational number " would be R and " r < sub > 0 </ sub > ( which is different from x ) is the smallest rational number " would be ¬ R.

It is common to use this first type of argument with propositions such as the one above, concerning the non-existence of some mathematical object.

Thus, as per Draper's argument above, the theory that there is an omniscient and omnipotent being who is indifferent requires no hidden reasons in order to explain evil.

The criterion, given above for the solvability of the word problem in a single group can be extended to a criterion for the uniform solvability of the word problem for a class of finitely presented groups by a straightforward argument.

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.

The Senate quickly met and began debating a change of government, but this eventually devolved into an argument over which of them would be the new princeps.

When she began work on this project in 1873, most Americans thought the U. S. would never again face a calamity like the Civil War, but Barton finally succeeded during the administration of President Chester Arthur, using the argument that the new American Red Cross could respond to crises other than war.

In Santa Clara County v. Southern Pacific Railroad, 118 U. S. 394 ( 1886 ), the reporter noted in the headnote to the opinion that the Chief Justice began oral argument by stating, " The court does not wish to hear argument on the question whether the provision in the Fourteenth Amendment to the Constitution, which forbids a State to deny to any person within its jurisdiction the equal protection of the laws, applies to these corporations.

Following Haug, the Bombay Parsis began to defend themselves in the English language press ; the argument being that Angra Mainyu was not Mazda's binary opposite, but his subordinate, who — as in Zurvanism also — chose to be evil.

However, an argument began as to who should take the boar's skin as a prise: Meleager gave it to Atalanta, but two of his maternal uncles, sons of Thestius, wanted the trophy for themselves, claiming that it belonged to them by the right of birth if Meleager did not want it.

Taking human form, the Bagadjimbiri began an argument with Ngariman, a cat-person.

The incident began with an argument between two local lawmen, Billy Bailey and Mike McCluskie.

" After an argument with his mother, with whom he had an often volatile relationship, Burke was evicted from his home and began living on the streets of North Philadelphia in 1957.

in the California Railroad Tax cases expresses with sufficient accuracy what was said before the argument began.

This transition began with motions in limine, to exclude evidence, on which it was felt the jury should not hear the argument because they would be informed of the evidence to be excluded.

" He was not a man of many words ," says Clarendon, " and rarely began the discourse or made the first entrance upon any business that was assumed, but a very weighty speaker, and after he had heard a full debate and observed how the House was likely to be inclined, took up the argument and shortly and clearly and craftily so stated it that he commonly conducted it to the conclusion he desired ; and if he found he could not do that, he never was without the dexterity to divert the debate to another time, and to prevent the determining anything in the negative which might prove inconvenient in the future " ( Hist.

Santa Clara County v. Southern Pacific Railroad is sometimes cited for this finding because the court reporter's comments included a statement the Chief Justice made before oral arguments began, telling the attorneys during pre-trial that " the court does not wish to hear argument on the question whether the provision in the Fourteenth Amendment to the Constitution, which forbids a State to deny any person within its jurisdiction the equal protection of the laws, applies to these corporations.

On April 1, 1984, Gay began arguing with his wife over an important insurance policy that was missing ; the argument had started the previous night.

The argument lifted from the German paper began by stating that New Guinea fell into the Australian sphere but had been neglected ; although the Portuguese had explored in the 16th century, it was the Dutch from the 17th century " who seemed better satisfied with the country than other European nations had been " but they had overreached themselves and had fallen back towards Java, Sumatra and Celebes.

By the end of 1980, the number of TSS cases reported to the CDC began to decline, however there is some argument as to whether statistics provided by CDC are reliable due to problems with recognition of TSS symptoms by medical staff and the way in which CDC records TSS cases, many estimate that only around a third of all TSS cases reported to the CDC were included in statistics.

However, in the third film, when his ancestor Seamus McFly points out that Seamus's brother, Martin, was killed in an argument where someone questioned his bravery, Marty began to re-think his stance on what other people thought of him.

The following week at the Illinois Republican convention in Springfield, Bush began to press the argument against Dukakis by declaring that Dukakis had let Horton loose to ' terrorize innocent people ' and continued support of the furlough program until the Massachusetts legislature changed the law.

One night in 1973 Weaver threw his cap to the ground and began a vehement argument with Luciano.

In the Descent of Man, Darwin wrote that by choosing tools and weapons over the years, " man has ultimately become superior to woman " but Blackwell's argument for women's equality went largely ignored until the 1970s when feminist scientists and historians began to explore Darwin.

As 1872 began, Mivart politely inflamed the argument again, writing " wishing you very sincerely a happy new year " while wanting a disclaimer of the " fundamental intellectual errors " in the Descent of Man.

He relates in his autobiography that he wanted to cast Timothy Dalton for Christopher Columbus: The Discovery but that Dalton left the project before shooting began ; Glen wonders if-following an argument at the end of shooting on Licence to Kill-Dalton did not wish to appear in another of his films.

Although this group would play their own material, the band split up after an argument between the singer and the guitarist, and McBrain began playing with Billy Day, a singer and keyboardist, and Michael " Mickey " Lesley, a guitarist, in 1971.