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.

and the success of such an endeavor is, as suggested above, glaringly rare.

This is what was meant, above, by describing history as inferential.

Its success is a tribute, above all, to Trevelyan's brilliance as a literary stylist.

It is but justice to Mr. Steele for us to add that, in the above remarks, nothing is intended to his disparagement, either as a lawyer or as a printer.

Actually it amounts to $1,250,000 above what the institution already is receiving, considering the additional half-million dollars Gov. Vandiver allocated last year from the state surplus.

Khrushchev, for all his bombastic prophecies about the inevitable decay of capitalism, is genuinely favorable to `` peaceful coexistence '' and would like, above all, the Berlin and German problems to be settled peacefully ; ;

The credit provdied by the first two services in the system outlined above is primarily for general agricultural purposes.

Expansion and relocation of industry in Rhode Island is the direct responsibility of the Development Council's Industrial Division, and the figures quoted above indicate a successful year's operation.

In all other States it is the difference obtained by subtracting from 100 the result obtained in item 4 above ; ;

Determine if the particular State's unadjusted allotment ( result obtained in item 11 above ) is greater than its maximum allotment, and if so lower its unadjusted allotment to its maximum allotment.

Determine if the particular State's unadjusted allotment ( result obtained in item 11 above ) is less than its minimum ( base ) allotment, and if so raise its unadjusted allotment to its minimum allotment.

The funds recouped by reductions in item 12 above are used: first, to increase the unadjusted allotments to the specified minimum in those States where the unadjusted allotment is less than the minimum allotment ( item 13 above ) ; ;

In all other States it is the difference obtained by subtracting from 100 the result obtained in item 4 above ; ;

It is agreed that any goods delivered or services rendered after the date of this agreement for projects within categories A, B, and C under paragraph 2 above which may later be approved by the United States will be eligible for financing from currency granted or loaned to the Government of India.

I therefore believe it is realistic to assume a modest drop in the total value of home entertainment electronics to about $1.8 million, slightly below 1960, but above 1959.

The symbol for division is a straight line that separates two numbers placed one above the other.

Flash is allowed, subject to above restrictions.

Foliage is the outstanding photo subject in many of the Southern locales mentioned above and some specific tips on how and where to shoot it are in order.

The sink in the hinged panel above the bunk drains into the head and a five-gallon water tank is mounted on the bulkhead above the sink.

whose chord is one hundred and sixty feet, and whose vortex is forty feet ( it was actually 37 feet ) above the high-water mark.

Even if you live above that line, the FHA will back you, for they have decided that the inclusion of air conditioning in all new homes is a good thing and should be encouraged.