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 began by giving an unavoidable set of five configurations ( a single vertex with degree 1, a single vertex with degree 2, ..., a single vertex with degree 5 ) and then proceeded to show that the first 4 are reducible ; to exhibit an unavoidable set of configurations where every configuration in the set is reducible would prove the 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.

But this argument cannot be pushed very far because the Communist system makes up for any shortcomings of its leaders in respect to corrosion.

She makes the argument that grouping all people of African descent together regardless of their unique ancestral circumstances would inevitably deny the lingering effects of slavery within the American community of slave descendents, in addition to denying black immigrants recognition of their own unique ancestral backgrounds.

One argument in the field of philosophy of consciousness deals with what it is that makes a mental state “ conscious ” in the sense of there being something it is like to experience that state.

Other historicists have seen no significance in the date that Revelation was written, and have even held to an early date while Kenneth L. Gentry, Jr., makes an exegetical and historical argument for the pre-AD 70 composition of Revelation.

Partial application makes it easy to define these functions, for example by creating a function that represents the addition operator with 1 bound as its first argument.

The argument against disclosure is that providing complete details or tools to malicious attackers, such as black hats and script kiddies, allows them to take advantage of vulnerabilities more quickly and makes attacks more widespread.

A separate argument from silence against the total or partial authenticity of the Testimonium is that a 5th or 6th century table of contents of Josephus ( although selective ) makes no mention of it.

Singer's most recent book, The Life You Can Save, makes the argument that it is a clear-cut moral imperative for citizens of developed countries to give more to charitable causes that help the poor.

One argument states that Plautus writes with originality and creativity — the other, that Plautus is a copycat of Greek New Comedy and that he makes no original contribution to playwriting.

Yogananda makes an argument for the mystical basis of Khayyam's Rubaiyat.

The argument that the textures achieved with CGI cannot match the way real textures are captured by stop motion also makes it valuable for a handful of movie makers, notably Tim Burton, whose puppet-animated film Corpse Bride was released in 2005.

Similarly, for every hidden argument that completely or partially justifies observed evils it is equally likely that there is a hidden argument that actually makes the observed evils worse than they appear without hidden arguments.

In A Social History of Truth ( 1994 ), for example, Steven Shapin makes the largely sociological argument that, in 17th-century England, the mode of sociability known as civility became the primary discourse of truth ; for a statement to have the potential to be considered true, it had to be expressed according to the rules of civil society.

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.

Rewriting the argument,, makes clear that this expression describes a vibration of wavelength traveling in the x-direction with a constant phase velocity.

John Nash proved in 1952 that a game of Hex cannot end in a tie, and that for a symmetric board there exists a winning strategy for the player who makes the first move ( by the strategy-stealing argument ).

", Plotinus makes the argument that specific stars influencing one's fortune ( a common hellenistic theme ) attributes irrationality to a perfect universe, and invites moral turpitude.

Miller seems to build from Bitzer's argument regarding what makes something rhetorical, which is the ability of change to occur.

The first recorded mention of the idea was by Zhuangzi, and it is also discussed in Hinduism, which makes extensive use of the argument in its writings.

Robert D. Putnam, in his book Bowling Alone makes the argument that social capital is linked to the recent decline in American political participation.

He also makes an argument, after studying the Arab histories of the period, that these were clearly armies of invasion, sent by the Caliph not just to avenge Tours, but to begin the end of Christian Europe and bring it into the Caliphate.

When Sir Joseph makes the argument that " love levels all ranks ", a delighted Josephine says that she " will hesitate no longer ".

Jody Rosen counters Brooks ' argument, criticizing Brooks makes use of only a few, old samples of potential French gangsta rap that contain violent or misogynistic lyrics.

If all surviving societies have found it necessary to impose some of the same restrictions upon the behavior of their members, this makes a strong argument that these aspects of the moral code are indispensable.