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Page "Countable set" ¶ 16
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is and where
But California is where we're goin ''.
He thought of the jungles below him, and of the wild, strange, untracked beauty there and he promised himself that someday he would return, on foot perhaps, to hunt in this last corner of the world where man is sometimes himself the hunted, and animals the lords.
Now I wish to enter the American market, where the competition is very strong.
from downstream, where the water level is much lower, it is a high, elaborately facaded pavilion.
The answers derived by these means may determine not only the temporal organization of the dance but also its spatial design, special slips designating the location on the stage where the movement is to be performed.
Even in domains where detailed and predictive understanding is still lacking, but where some explanations are possible, as with lightning and weather and earthquakes, the appropriate kind of human action has been more adequately indicated.
Robert Penn Warren puts it this way in `` Brother To Dragons '': `` The recognition of complicity is the beginning of innocence '', where innocence, I think, means about the same thing as redemption.
A dominant motive is the poet's longing for his homeland and its boyhood associations: `` Not men-folk, but the fields where I would stray, The stones where as a child I used to play ''.
In a society where everything is for sale, Marlowe is the only man who cannot be bought.
This is done for simplicity of commands and to bring the hidden redundancy up to where misunderstanding has almost zero possibility.
As to benefits to employees, it is notorious for its callous disregard except where it depends on them for services.
`` The Moral Creed '' and `` The Will To Risk '' live happily together, if we do not examine where the line is to be drawn.
Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.
Ptolemy's problem is to forecast where, against the inverted bowl of night, some particular light will be found at future times.
She was exposing herself to temptation which it is best to avoid where it can consistently be done.
Such performance is a great tribute to American scientists and engineers, who in the past five years have had to telescope time and technology to develop these long-range ballistic missiles, where America had none before.
but it is perennially restructured in situations where anchors are dragged or lost.
`` History has this in common with every other science: that the historian is not allowed to claim any single piece of knowledge, except where he can justify his claim by exhibiting to himself in the first place, and secondly to any one else who is both able and willing to follow his demonstration, the grounds upon which it is based.
Finally we may note that the idea appears in educational theory where its influence is at present widespread.

is and concept
A concept of responsibility is in process of articulation and establishment.
National responsibility for individual welfare is a concept not limited to the United States or even to the Western nations.
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 ''.
Whether a concept analogous to the principle of internal responsibility operates in a nation's external relations is less obvious and more difficult to establish.
) The concept of nationalism is the political principle that epitomizes and glorifies the territorial state as the characteristic type of socal structure.
Historically, however, the concept is one that has been of marked benefit to the people of the Western civilizational group.
But it is more than irony: one of the main reasons why nationalism is no longer a tenable concept is because it has spread throughout the planet.
It is interesting, however, that despite this strong upsurge in Southern writing, almost none of the writers has forsaken the firmly entrenched concept of the white-suited big-daddy colonel sipping a mint julep as he silently recounts the revenue from the season's cotton and tobacco crops ; ;
A broader concept of imitation is needed, one which acknowledges that true invention is important, that the artist's creativity in part transcends the non-artistic causal factors out of which it arises.
Who will deny that in a vast portion of the South the Federal action is incompatible with the Jeffersonian concept of `` the consent of the governed ''??
For it is their catastrophic concept of the Anglo-Saxon invasions rather than Kemble's gradualist approach which dominates the field.
But beginning, for all practical purposes, with Frederick Seebohm's English Village Community scholars have had to reckon with a theory involving institutional and agrarian continuity between Roman and Anglo-Saxon times which is completely at odds with the reigning concept of the Anglo-Saxon invasions.
It is ironic that Washington is having to struggle so for a concept that for six years it bypassed as unreasonable.
The concept of labor as a special class is outmoded, and in the task confronting America as bastion of the free world, labor must learn to put the national interest first if it is itself to survive.
The most fundamental concept of the new approach to economic aid is the focusing of our attention, our resources, and our energies on the effort to promote the economic and social development of the less developed countries.
While it is easy enough to ridicule Hawkins' pronouncement in Pleas Of The Crown from a metaphysical point of view, the concept of the `` oneness '' of a married couple may reflect an abiding belief that the communion between husband and wife is such that their actions are not always to be regarded by the criminal law as if there were no marriage.
That we had the wit and wisdom to adopt Mr. Lowell's concept and make it the base for our processes of selection is one reason why our selections have been, it may be said truly, pretty uniformly good.
It is this sort of experience that makes the concept of high fidelity of real musical significance for the home music listener.
The concept of trans-illumination ( as shown by the photo on p. 92 ), as just one example, offers an entirely new approach to lighting problems -- no matter what industry is involved.

is and bijection
Since a maximal ideal in A is closed, is a Banach algebra that is a field, and it follows from the Gelfand-Mazur theorem that there is a bijection between the set of all maximal ideals of A and the set Δ ( A ) of all nonzero homomorphisms from A to C. The set Δ ( A ) is called the " structure space " or " character space " of A, and its members " characters.
A set S is called countable if there exists an injective function f from S to the natural numbers Since there is an obvious bijection between and it makes no difference whether one considers 0 to be a natural number of not.
What we have done here is arranged the integers and the odd integers into a one-to-one correspondence ( or bijection ), which is a function that maps between two sets such that each element of each set corresponds to a single element in the other set.
Two sets have the same cardinal number if and only if there is a bijection between them.
If f is a surjection and a ~ b ↔ f ( a ) = f ( b ), then g is a bijection.
Thus there is a natural bijection from the set of all possible equivalence relations on X and the set of all partitions of X.
Formally, a set S is called finite if there exists a bijection
Thus it is a bijection such that
Another way to describe G-sets is the functor category, where is the groupoid ( category ) with one element and isomorphic to the group G. Indeed, every functor F of this category defines a set X = F and for every g in G ( i. e. for every morphism in ) induces a bijection F < sub > g </ sub >: X → X.
* f is a bijection ( one-to-one and onto ),
This mapping is one-to-one and onto, that is, it is a bijection from the domain to the codomain of the logarithm function.
In mathematical analysis, an isomorphism between two Hilbert spaces is a bijection preserving addition, scalar multiplication, and inner product.
Such a function is called a one-to-one correspondence or a bijection, and has the property that every element corresponds to exactly one element.
In order for a compression algorithm to be considered lossless, there needs to exist a reverse mapping from compressed bit sequences to original bit sequences ; that is to say, the compression method would need to encapsulate a bijection between " plain " and " compressed " bit sequences.

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