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Page "Ramsey's theorem" ¶ 27
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2-color and if
Conversely, the symbol width could be set at 8, even if only values 0 and 1 are used ; these data would only require a 2-color table.

2-color and are
Some of the earliest 2-color Technicolor tests were shot at his Beverly Hills home ( These are included as extra material in the Harold Lloyd Comedy Collection DVD Box Set ).
Vexels are often characterized by crisp, clean color and lines ( that look nearly vector-graphics style ) but is entirely pixel-based, with a variety of color levels, from 2-color outlines to pseudo-realism.
The 5-color and 2-color Dogics are even less of a challenge, since there is a large number of identical pieces.

case and if
Just as in the case of every prodigy child, we must watch for the efficacy of my teaching to show up in the future -- if he should master all the strenuous exercises I inflicted on him.
We can be virtuous only if we control our lower natures, the passions in this case, and strengthen our rational side ; ;
But if she were just having a normal case of pre-nuptial jitters such a question might frighten her out of a really good marriage.
But if true, it was the case of which he had dreamed, the case which would throw him into headlines all over America as the hero of a great murder trial.
But if this is the case, then an arbitrary pencil of lines having a point, P, of **zg as vertex is transformed into a ruled surface of order Af having Af generators concurrent at P.
For if such were the case, either the plane of the two lines would meet **zg in more than K points or, alternatively, the order of the image regulus of the pencil determined by the two lines would be too high.
We now observe that the case in which **zg is a Af curve on a quadric is impossible if the complex of singular lines consists exclusively of the lines which meet Aj.
If anyone asked us, after we made the remark that the suffering was a bad thing, whether we should think it relevant to what we said to learn that the incident had never occurred and no pain had been suffered at all, we should say that it made all the difference in the world, that what we were asserting to be bad was precisely the suffering we thought had occurred back there, that if this had not occurred, there was nothing left to be bad, and that our assertion was in that case mistaken.
In the specific case of time diffusion, we must emphasize the significance of the earlier development of mistrust when it is combined with the inevitable time crisis experienced by most ( if not all ) adolescents in our society, and with the failure of the adolescent period to provide opportunities for developing trust.
William A. Redding asserted that if the case had been heard in open court under rules of evidence, the testimony would have been completed in sixty days instead of five years.
One of the A.L.A.M. lawyers observed that if the Selden case had been tried under this simplified procedure, the testimony which filled more than a score of volumes, `` at a minimum cost of $1 a page for publication alone, could have been contained in one volume ''.
`` What this amounts to, if true, is that there will be a free-for-all fight in this case.
After reading his statement discharging the 23d ward case, Karns told Wexler that if the seven cases scheduled for trial also involved persons who had been subpenaed, he would dismiss them.
He asked members of the panel to tell him if anyone outside the court had spoken to them about the case.
Thus, if what is at issue is whether `` All S is P '', it is indifferent whether `` Some S is not P '' or `` No S is P '', since in either case the judgment in question is false.
In any case, though they had been promised immortality if they ate of the tree, they obtained mortality instead.
Presumably, if the reverse is the case and the good effect is more certain than the evil result that may be forthcoming, not only must the good and the evil be prudentially weighed and found proportionate, but also calculation of the probabilities and of the degree of certainty or uncertainty in the good or evil effect must be taken into account.
A simple illustration of such cause and effect is the case of experiencing the effects of what I cause: if I cause suffering, then as a natural consequence I will experience suffering ; if I cause happiness, then as a natural consequence I will experience happiness.
This might be the proper standard of review, for example, if the lower court resolved the case by granting a pre-trial motion to dismiss or motion for summary judgment which is usually based only upon written submissions to the trial court and not on any trial testimony.
The first function is assumed, if the expression in the argument contains more characters or, than characters, and the second function is assumed in the opposite case.
In many cases such a selection can be made without invoking the axiom of choice ; this is in particular the case if the number of bins is finite, or if a selection rule is available: a distinguishing property that happens to hold for exactly one object in each bin.
In that case it is equivalent to saying that if we have several ( a finite number of ) boxes, each containing at least one item, then we can choose exactly one item from each box.

case and R
In this case the stage R operating with conditions Af transforms the state of the stream from Af to Af, but only the probability distribution of Af is known.
In the case of the complex numbers, C, there is a unique nontrivial automorphism that sends R into R: complex conjugation, but there are infinitely ( uncountably ) many " wild " automorphisms ( assuming the axiom of choice ).
The case was legally resolved on October 19, 1973 when U. S. District Judge Earl R. Larson held the ENIAC patent invalid, ruling that the ENIAC derived many basic ideas from the Atanasoff – Berry Computer.
* If the balance factor of R is-1, a single left rotation ( with P as the root ) is needed ( Right-Right case ).
The Lord's Day Act, which since 1906 had prohibited business transactions from taking place on Sundays, was struck down as unconstitutional in the 1985 case R. v. Big M Drug Mart Ltd. Calgary police officers witnessed several transactions at the Big M Drug Mart, all of which occurred on a Sunday.
A binary relation is the special case of an n-ary relation R ⊆ A < sub > 1 </ sub > × … × A < sub > n </ sub >, that is, a set of n-tuples where the jth component of each n-tuple is taken from the jth domain A < sub > j </ sub > of the relation.
The English case of R v. Coney in 1882 found that a bare-knuckle fight was an assault occasioning actual bodily harm, despite the consent of the participants.
In this case, is the smallest σ-algebra that contains the open intervals of R. While there are many Borel measures μ, the choice of Borel measure which assigns for every interval is sometimes called " the " Borel measure on R. In practice, even " the " Borel measure is not the most useful measure defined on the σ-algebra of Borel sets ; indeed, the Lebesgue measure is an extension of " the " Borel measure which possesses the crucial property that it is a complete measure ( unlike the Borel measure ).
For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies
The case of R v Dudley and Stephens, in which two men were found guilty of murder for killing and eating a cabin boy while adrift at sea in a lifeboat, set the precedent that necessity is no defence to a charge of murder.
The case of R v. Dudley and Stephens ( 1884 ) 14 QBD 273 ( QB ) is an English case which dealt with four crew members of an English yacht, the Mignonette, who were cast away in a storm some from the Cape of Good Hope.
where vertical bars |...| denote the vector magnitude, which in the case of r ( t ) is simply the radius R of the path.
Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.
This meant to look at these concepts from the standpoint of the paradigm of critical psychology, thereby integrating their useful insights into critical psychology while at the same time identifying and criticizing their limiting implications while ( which in the case of S – R psychology were the rhetorical elimination of the subject and intentional action, and in the case of cognitive psychology which did take into account subjective motives and intentional actions, methodological individualism ).
This was confirmed in the case of R v Carroll, where the police found new evidence convincingly disproving Carroll's sworn alibi two decades after he had been acquitted of murder charges in the death of Ipswich child Deidre Kennedy, and successfully prosecuted him for perjury.
One can express the divergence as a particular case of the exterior derivative, which takes a 2-form to a 3-form in R < sup > 3 </ sup >.
An ellipse ( in red ) as a special case of the hypotrochoid with R = 2r.
The ellipse is a special case of the hypotrochoid when R = 2r.

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