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 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.

Concordant with the above understanding, any assertion about the motion of a body boils down to a description over time in which the body under consideration is at t < sub > 1 </ sub > found in the vicinity of one group of " landmark " bodies and at some t < sub > 2 </ sub > is found in the vicinity of some other " landmark " body or bodies.

Leader André Breton was explicit in his assertion that Surrealism was above all a revolutionary movement.

There are various questions that can be asked about the above indeterminacy assertion.

In the true sense of the word, according to the axioms established above for the reliability of historical tradition, there can be only assertion of real prophecy when the divine revelations apply to important public matters ; while those revelations which pertain to less important matters, or even to the personal affairs of a single individual, can not be classed under this head ( ib.

He furnishes empirical evidence as proof for this assertion ; different seasons are marked by particular arrangements of the planets and stars ( most notably the sun ); the appearance and manner of people varies according to the arrangement of heavenly bodies situated above their homeland.

Of Dr. Ross's assertion above, he says about possible pagan origins " What can be said against it, is that it is less easily proved and can be less easily illustrated than the possible continental, French origin for the motif discussed in earlier chapters ...." ( The Witch on the Wall page 95 ).

In fact associativity follows ; moreover, condition 1 above can be weakened to the assertion that both operations are unital, since it can be proved from condition 2 that the units must then coincide.

As mentioned above, 6, 603 is typically taken to represent the number of inhabitants of the cacique, Nicoya ’ s town, but Cereceda never makes that assertion, only that they baptized that number of people.

The above assertion is not true for general non-negative irreducible matrices.

Leader André Breton was explicit in his assertion that Surrealism was above all a revolutionary movement.

Besides the above, he published many works on antiquarian, economic and other subjects, including L ' Uomo libero, in confutation of Rousseau's Contrat Social ; an attack upon the abbe Tartarotti's assertion of the existence of magicians ; Observazioni sulla musica antica e moderna ; and several poems.

When all forms of proposition are included the analysis is more complicated but not essentially different ; and it is clear that the problem is not as to the nature of truth and falsehood, but as to the nature of judgment or assertion, for what is difficult to analyse in the above formulation is ' He asserts aRb '.

The assertion that Calidheamh soluis is " a symbol of Ireland attributed in oral tradition to Cúchulainn " ( Mackillop ) does not seem very representative, since in the body of folktales that mention the sword of light ( listed above ), few ( if any ) names Cuchulainn as the protagonist.

According to the research report " Social and Economic Analysis of the Moree Community " released by Cotton Catchment Communities CRC which contradicts the above assertion 04: 47, 22 August 2011 ( UTC ):

On the remainder of the clear channels, the dominant ( class 1 ) -- B stations are protected as described above, and the relatively small number of secondary ( class 2 ) ) stations permitted to operate on these channels at night are required to operate directionally and/or with reduced power so as to protect the class 1, stations.

Each point on C, as a vertex, may possess a finite number of corresponding diagonal points by the above construction.

The numbers of species cited above follow Frost and the total number of known amphibian species is approximately 7, 000, of which nearly 90 % are frogs.

He designates Abrasax more distinctly as " the power above all, and First Principle ," " the cause and first archetype " of all things ; and mentions that the Basilidians referred to 365 as the number of parts ( mele ) in the human body, as well as of days in the year.

* ERA — Earned run average: total number of earned runs ( see " ER " above ), multiplied by 9, divided by innings pitched

* WAR — Wins above replacement: a non-standard formula to calculate the number of wins a player contributes to his team over a " replacement-level player "

For example, the division example above is surjective ( or onto ) because every rational number may be expressed as a quotient of an integer and a natural number.

Each number is the sum of the two directly above it.

Non-avian dinosaur fossils are found only below the K – T boundary, indicating that they became extinct during the boundary event .< ref > A very small number of dinosaur fossils have been found above the K – T boundary, but they have been explained as reworked fossils, that is, fossils that have been eroded from their original locations then preserved in later sedimentary layers.

It was designed to fly below the enemy's radar at speeds above Mach 3 and carry a number of hydrogen bombs that it would drop on its path over enemy territory.

Once the ray either encounters a light source, or more probably once a set limiting number of bounces has been evaluated, then the surface illumination at that final point is evaluated using techniques described above, and the changes along the way through the various bounces evaluated to estimate a value observed at the point of view.

The Earnhardt team car, the RCR number 29 Chevrolet driven by Kevin Harvick, still always displays the Earnhardt stylized number 3 on the " B " posts ( metal portion on each side of the car to the rear of the front windows ) above the number 29.

The oval aluminium tag was stamped " DDR " ( Deutsche Demokratische Republik ) above the personal ID number ; this information was repeated on the bottom half, which was intended to be broken off in case of death.

France issues either a metallic rounded rectangle ( Army ) or disk ( Navy ), designed to be broken in half, bearing Family Name & First Name above the ID number.

The South Korean army issues two long, rectangular tags with oval ends, stamped ( in Korean letters ) with " Ryuk Gun " (" Army ") above personal number, with name below that and blood group at bottom.

It is possible that in Romania particularly where Hungarians live in large number the area called Transylvania above listed foods are known and made with dill, still they are Hungarian foods.

Based on the above, the number of revelations ( accounting for sections that are not revelations ) presented by each Community of Christ prophet, are as follows:

Not every number that we would informally say has been unambiguously described, is definable in the above sense.

The first digit of the number indicates the dive group as defined above.

The second digit indicates the direction of rotation – as above, the third is the number of half-somersaults, and the fourth is the number of half-twists:

where the above is one of the ways to write the nth Bell number.