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Page "Limit (category theory)" ¶ 70
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which and is
It is also possible, but equally doubtful, that he actually shot down the hundreds of men with which his legend credits him.
Let me pass over the trip to Sante Fe with something of the same speed which made Mrs. Roebuck `` wonduh if the wahtahm speed limit '' ( 35 m.p.h. ) `` is still in ee-faket ''.
The place is inhabited by several hundred warlike women who are anachronisms of the Twentieth Century -- stone age amazons who live in an all-female, matriarchal society which is self-sufficient ''.
It is the last of the three tests of manhood which the women impose, to discover if a male is worthy of survival there.
It took thirty of our women almost six moons to build this one, which is higher and stronger than the old one.
`` I'd like to know just which it is that those guys don't understand, the liquor or automobiles ''.
The woman eyed the youth with the avidity a coin collector might display toward a rare doubloon which is not yet in his collection.
It is these other differences between North and South -- other, that is, than those which concern discrimination or social welfare -- which I chiefly discuss herein.
It became the sole `` subject '' of `` international law '' ( a term which, it is pertinent to remember, was coined by Bentham ), a body of legal principle which by and large was made up of what Western nations could do in the world arena.
Of greater importance, however, is the content of those programs, which have had and are having enormous consequences for the American people.
Recognizing that the Rule of Law is `` a dynamic concept which should be employed not only to safeguard the civil and political rights of the individual in a free society '', the Congress asserted that it also included the responsibility `` to establish social, economic, educational and cultural conditions under which his legitimate aspirations and dignity may be realized ''.
For better or for worse, we all now live in welfare states, the organizing principle of which is collective responsibility for individual well-being.
That is particularly true of sovereignty when it is applied to democratic societies, in which `` popular '' sovereignty is said to exist, and in federal nations, in which the jobs of government are split.

which and natural
The youth with the snake had a natural pride and joy of life which appealed to the woman.
I fled, however, not from what might have been the natural fear of being unable to disguise from you that the things about my bridegroom -- in the sense you meant the word `` things '' -- which you had been galvanizing yourself to tell me as a painful part of your maternal duty were things which I had already insisted upon finding out for myself ( despite, I may now say, the unspeakable awkwardness of making the discovery on principle, yes, on principle, and in cold blood ) because I was resolved, as a modern woman, not to be a mollycoddle waiting for Life but to seize Life by the throat.
As the field on which my tent was pitched was a favorite natural playground for the kids of the neighborhood, I had made many friends among them, taking part in their after-school games and trying desperately to translate Grimm's Fairy Tales into an understandable French as we gathered around the fire in front of the tent.
His father was a professor at Hartford Theological Seminary, and from him he acquired a conviction, which he passed along to me, that there is in the universe of persons a moral law, the law of love, which is a natural law in the same sense as is the physical law.
After the seventeenth century the audience ceased to be an organic community to which these ideas and their attendant habits of figurative language would be natural or immediately familiar.
They react in obedience to an instinct or urge which has itself been impelled by natural law.
Graceful as his fencing and dancing lessons had taught him to be in addition to the natural grace of his slight, wiry frame, he cut enough of a figure to have evoked a nickname in the college, to which he himself referred in Prolusion 6::
In the earlier sessions there was plentiful discussion on the natural law, which Dr. William V. O'Brien of Georgetown University, advanced as the basis for widely acceptable ethical judgments on foreign policy.
It was only natural that Fletcher would strive for a position in which he could make the decisions.
If your pool is located on or near sloping ground, it may have natural drainage which is certainly more desirable than to be faced with the annual expense and labor of first pumping out the water and then scooping out all the debris.
Other natural features which can be of high interest are the forests, canyons, mountains, deserts, seacoast, beaches, sand dunes, waterfalls, springs, etcetera with which the area is blessed.
And like this English master, Mason realizes his subjects in large, simplified masses which, though they seem effortless, are in reality the result of skilled design born of hard work and a thorough distillation of the natural form that inspired them.
and natural waters, in addition, often contain impurities such as calcium salts which can react with soils to make them more difficult to remove.
The natural anatomical and physiological defensive features of the upper respiratory tract, such as the turbinates of the nose and the cilia of the trachea and larger bronchi, are capable of impinging out the larger particles to which we are ordinarily exposed in our daily existence.
It is natural from the marksman's viewpoint to call a bull's-eye a success, but in the mice example it is arbitrary which category corresponds to straight hair in a mouse.
We find it in the later Stoic conception of man's natural condition which included the community of all possessions.
Finally, the conception of the natural community of all possessions which originated with the Stoics was firmly fixed in a tradition by More's time, although it was not accepted by all the theologian-philosophers of the Middle Ages.
In a properly ordered society the massive force of public law performs the function which in natural law theory ineptly is left altogether to a small voice so often still.
the soap nut, which owes its sudsing power to natural saponins ; ;
It is natural that he should turn for his major support to a select and dedicated few from the organization which actually owns the university and whose goals are, in their opinion, identified with its highest good and ( to use that oft-repeated phrase ) ' the attainment of excellence ' ''.
If this aspect of death as punishment is not distinguished from the idea of death as natural termination, the conclusion seems inevitable that temporal existence itself is a form of punishment rather than the state into which man is put by the will of the Creator.
The importance of this 5 can largely be explained by the natural mathematical properties of the middle number and its special relationship to all the rest of the numbers -- quite apart from any numerological considerations, which is to say, any symbolic meaning arbitrarily assigned to it.

which and variables
Rather, such assignments are made, as they must be, on the basis of certain overall rules and standards, representing to some extent a statistical approach to the problem, taking into account for each situation some of the variables ( e.g., power and station separations ) and averaging out others in order to achieve the balance which must be struck between protection against destructive interference and the assignment of a number of stations large enough to afford optimum radio service to the Nation.
The several trials of a binomial experiment produce a new random variable X, the total number of successes, which is just the sum of the random variables associated with the single trials.
the way in which the transformation of state depends on the operating variables for the main types of reactors is discussed in the next chapter.
In mathematics, a binary function, or function of two variables, is a function which takes two inputs.
A generalization of the class of Horn formulae is that of renamable-Horn formulae, which is the set of formulae that can be placed in Horn form by replacing some variables with their respective negation.
from which it is clear that and for k > n. To see that these coefficients count k-combinations from S, one can first consider a collection of n distinct variables X < sub > s </ sub > labeled by the elements s of S, and expand the product over all elements of S:
The variables which determine climate are numerous and the interactions complex, but there is general agreement that the broad outlines are understood, at least insofar as the determinants of historical climate change are concerned.
Scheme introduced the sole use of lexically scoped variables to Lisp ; an inspiration from ALGOL 68 which was widely recognized as a good idea.
In Scheme, it is ( broadly ) necessary to avoid giving variables names which clash with functions ; Scheme functions frequently have arguments named,, or so as not to conflict with the system function.
If are independent and identically distributed random variables, each with a standard Cauchy distribution, then the sample mean has the same standard Cauchy distribution ( the sample median, which is not affected by extreme values, can be used as a measure of central tendency ).
They were codified by Francis Bacon, and developed further by John Stuart Mill and consist of controlling several variables, in turn, to establish which variables are causally connected.
Showing several variables allows comparison, which adds to the meaningfulness of the map.
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.
So assume ƒ is differentiable at 0, as a function of two real variables from Ω to C. This is equivalent to the existence of two complex numbers and ( which are the partial derivatives of ƒ ) such that we have the linear approximation
* Jones diagram, which plots four variables rather than two.
The sound of a drum depends on several variables, including shape, size and thickness of its shell, materials from which the shell was made, counterhoop material, type of drumhead used and tension applied to it, position of the drum, location, and the velocity and angle in which it is struck.
Quantitative measures of dependence include correlation ( such as Pearson's r when both variables are continuous, or Spearman's rho if one or both are not ) and covariance ( which reflects the scale upon which variables are measured ).
These include the number and types of the attributes or variables and the various statistical measures which may be applied to them such as standard deviation and kurtosis.
More subtle is the slight over-representation of string operations, which is largely language-related: both Ada and Pascal have strings as normal variables in the language, whereas C does not, so what was simple variable assignment in reference benchmarks became buffer copy operations in the C library.
DHTML allows scripting languages to change variables in a web page's definition language, which in turn affects the look and function of otherwise " static " HTML page content, after the page has been fully loaded and during the viewing process.

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