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fact and f
" f one regards the Modest Proposal simply as a criticism of condition, about all one can say is that conditions were bad and that Swift's irony brilliantly underscored this fact ".
More conceptually, this rule expresses the fact that a change in the x < sub > i </ sub > direction may change all of g < sub > 1 </ sub > through g < sub > k </ sub >, and any of these changes may affect f.
In this situation, the chain rule represents the fact that the derivative of is the composite of the derivative of f and the derivative of g. This theorem is an immediate consequence of the higher dimensional chain rule given above, and it has exactly the same formula.
Some genetic studies seem to prove a Celtic descendence of most inhabitants in the region, but not Germanic in fact, that is reinforced by the Gaulish toponyms such as those ending with the suffix-ago < Celtic -* ako ( n ) ( f. e.
If in the third identity we take H = G, we get that the set of commutators is stable under any endomorphism of G. This is in fact a generalization of the second identity, since we can take f to be the conjugation automorphism.
Similarly, the fact that d ( f dz )
In fact, her voice could reach down to f < sub > 3 </ sub > only while practising: in public her lowest note was g < sub > 3 </ sub >.
This symmetry results from the mathematical fact that the density of electrons f ( r ) at a position r is always a real number.
The proof follows by the fact that if f were indeed a map onto P ( S )), then we could find r in S, such that f (
Given parallel morphisms f and g, the equaliser of f and g is just the kernel of g − f, if either exists, and the analogous fact is true for coequalisers.
More precisely, the Roche limit is determined by the fact that the function f, which can be regarded as a nonlinear measure of the force squeezing the ellipsoid towards a spherical shape, is bounded so that there is an eccentricity at which this contracting force becomes maximal.
As was shown by Goursat, Cauchy's integral theorem can be proven assuming only that the complex derivative f '( z ) exists everywhere in U. This is significant, because one can then prove Cauchy's integral formula for these functions, and from that deduce these functions are in fact infinitely differentiable.
In fact, the parallel of f is an isomorphism for every morphism f if and only if the pre-abelian category is an abelian category.
If f is assumed to be continuous as well then this can be extended to show that homogeneity for α any real number, using the fact that rationals form a dense subset of the reals.
In the category of groups, a monomorphism f from H to G is normal if and only if its image is a normal subgroup of G. In particular, if H is a subgroup of G, then the inclusion map i from H to G is a monomorphism, and will be normal if and only if H is a normal subgroup of G. In fact, this is the origin of the term " normal " for monomorphisms.
Upon closer inspection, it can be seen that in fact, the Scheme example above uses a quine, and f ( x ) is actually the quine function itself.
For an instrument whose payment stream is described by f ( t ), the value V ( t ) satisfies the inhomogeneous first-order ODE (" inhomogeneous " is because one has f rather than 0, and " first-order " is because one has first derivatives but no higher derivatives ) – this encodes the fact that when any cash flow occurs, the value of the instrument changes by the value of the cash flow ( if you receive a $ 10 coupon, the remaining value decreases by exactly $ 10 ).
In fact, the sum of the angles of a triangle on a sphere is 180 °( 1 + 4f ), where f is the fraction of the sphere's surface that is enclosed by the triangle.
Since f ( X ) is irreducible, ( f ( X )) is a maximal ideal and hence is, in fact, a field.

fact and coincides
In around 500 BCE, after the Zhou state weakened and China moved into the Spring and Autumn Period, the classic period of Chinese philosophy began ( it is an interesting fact that this date nearly coincides with the emergence of the first Greek philosophers ).
The fact that the class of complex analytic functions coincides with the class of holomorphic functions is a major theorem in complex analysis.
This fact could be useful in proving the Euler line of the intouch triangle of a triangle coincides with its OI line.
The Eastern Orthodox Church, Oriental Orthodoxy and Eastern Catholic Churches do not move the feast, having special combined liturgies for those years when the Annunciation coincides with another feast ; in fact in these churches a Divine Liturgy is celebrated on Good Friday when it coincides with the Annunciation.
This coincides very well with the fact, that the land belonging to Sørvág is divided into three parts: Suðurtriðingur, Norðurtriðingur and Úttriðingur.

fact and with
The mere fact that the tall figure with the rifle and field glasses had been seen riding that way was enough to frighten three rustling homesteaders out of the Upper Laramie country in a single week.
And, as a matter of fact, Nicolas had slept in the park only part of one night, when he discovered that Munich's early mornings even in summer are laden with dew.
In fact it has caused us to give serious thought to moving our residence south, because it is not easy for the most objective Southerner to sit calmly by when his host is telling a roomful of people that the only way to deal with Southerners who oppose integration is to send in troops and shoot the bastards down.
Also, we should not even to-day discount the fact that a region such as the coastal lowlands centering on Charleston had closer ties with England and the West Indies than with the North even after independence.
In point of fact, this is a beige box with a bright red door, about one and a half feet square and hung from the wall about six feet from the door to Wisman's right.
In the incessant struggle with recalcitrant political fact he learns to focus the essence of a problem in the significant detail, and to articulate the distinctions which clarify the detail as significant, with what is sometimes astounding rapidity.
That is not to deny that he has been aware of traditions, of course, that he is steeped in them, in fact, or that he has dealt with them, in his books.
This, conjoined with the considerations above, made the circular motions of heavenly bodies appear an almost directly observed fact.
Whether you experienced the passion of desire I have, of course, no way of knowing, nor indeed have I wished with even the most fleeting fragment of a wish to know, for the fact that one constitutes by one's mere existence so to speak the proof of some sort of passion makes any speculation upon this part of one's parents' experience more immodest, more scandalizing, more deeply unwelcome than an obscenity from a stranger.
To you, for instance, the word innocence, in this connotation, probably retained its Biblical, or should I say technical sense, and therefore I suppose I must make myself quite clear by saying that I lost -- or rather handed over -- what you would have considered to be my innocence two weeks before I was legally entitled, and in fact by oath required, to hand it over along with what other goods and bads I had.
By this time she had learned that it was futile to argue with her young husband, yet the uncomfortable fact remained: the American Congregationalists were sending them as missionaries to the Far East and paying their salaries.
They were in fact quietly laughing at him, for their King wished to have nothing to do with the Western world.
When he discovered they had received from the Company's Court of Directors no permission to live in India, coupled with the fact that they were Americans who had been sent to Asia to convert `` the heathen '', he became more belligerent than ever.
His point is simply that the Tories have showered him with personal satire, despite the fact that as a private subject he has a right to speak on political matters without affronting the prerogative of the Sovereign.
This finding is consistent also with the fact that student leaders are more likely to be supporters of the values implicit in civil liberties than the other students.
Underneath all the high-sounding phrases of royal and papal letters and behind the more down-to-earth instructions to the envoys was the inescapable fact that Edward would have to desert his Flemish allies and leave them to the vengeance of their indignant suzerain, the king of France, in return for being given an equally free hand with the insubordinate Scots.
the mere fact that he was selected, though as a substitute, to act as interlocutor or moderator for it, or perhaps we should say with Buck as ' father of the act ', is in itself a difficult phase of his development to grasp.
But if anything can bring home to Mr. Khrushchev the idea that he will not really get much enjoyment from watching this Braddock-against-the-Indians contest, it will probably be the fact that SEATO forces are ready to attempt it -- plus the fact that Moscow has something to lose from closing off disarmament and other bigger negotiations with Washington.
It is in fact entirely consistent with your suggestion of modest industrial development to help pay governmental costs.
It seems that Khrushchev himself took a very special pride in having made a world-shaking contribution to Marxist doctrine with his Draft Program ( a large part of his twelve-hour speech at the recent Congress was, in fact, very largely a rehash of that interminable document ).
in fact, with having been against all the more popular features of the Khrushchev `` welfare state ''.
His views, in fact, coincide with those of foreign enemies of peaceful coexistence, who look upon it merely as a variant of the `` cold war '' or of an `` armed peace ''.

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