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Page "Word problem for groups" ¶ 71
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is and if
`` That is, if we can be sure this is Colcord's money '' --
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 ''.
It is the last of the three tests of manhood which the women impose, to discover if a male is worthy of survival there.
There was a measure of protection in its concrete walls and ceiling, but the engineers who hastily installed it were well aware that concrete is not much better than prayer, if as efficacious, when a direct hit comes along.
`` And if the dive goes OK he has the exclusive import rights to your line for this country, is that right ''??
`` All right, if you can't do your arithmetic during school hours you can do it after school is out '', Miss Langford said firmly, not smiling.
Why, in the first place, call himself a liberal if he is against laissez-faire and favors an authoritarian central government with womb-to-tomb controls over everybody??
And if he is so scornful of the rights of states, why not advocate a different sort of constitution that he could more sincerely support??
If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.
I think it is essential, however, to pinpoint here the difference between the two concepts of sovereignty that went to war in 1861 -- if only to see better how imperative is our need today to clarify completely our far worse confusion on this subject.
Unruly hair goes straight up from his forehead, standing so high that the top falls gently over, as if to show that it really is hair and not bristle.
If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.
He will not curb his instinctual desires but release the energy within him that makes him feel truly and fully alive, even if it is only for this brief moment before the apocalypse of annihilation explodes on earth.
If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.
And if I have gone into so much detail about so small a work, that is because it is also so typical a work, representing the germinal form of a conflict which remains essential in Mann's writing: the crude sketch of Piepsam contains, in its critical, destructive and self-destructive tendencies, much that is enlarged and illuminated in the figures of, for instance, Naphta and Leverkuhn.
All such imitations of negative quality have given rise to a compensatory response in the form of a heroic and highly individualistic humanism: if man can neither know nor love reality as it is, he can at least invent an artistic `` reality '' which is its own world and which can speak to man of purely personal and subjective qualities capable of being known and worthy of being loved.
But Aristotle kept the principle of levels and even augmented it by describing in the Poetics what kinds of character and action must be imitated if the play is to be a vehicle of serious and important human truths.
Operating as a one man police force in fact if not in name, he is at once more independent and more dedicated than the police themselves.

is and G
It is easily seen that Af divides G.
The angle generated by the platform servo **yf multiplied by G is the effective acceleration acting on the accelerometer.
Although there are seven other types of annual awards presented by the Academy ( the Irving G. Thalberg Memorial Award, the Jean Hersholt Humanitarian Award, the Gordon E. Sawyer Award, the Scientific and Engineering Award, the Technical Achievement Award, the John A. Bonner Medal of Commendation, and the Student Academy Award ) plus two awards that are not presented annually ( the Special Achievement Award in the form of an Oscar statuette and the Honorary Award that may or may not be in the form of an Oscar statuette ), the best known one is the Academy Award of Merit more popularly known as the Oscar statuette.
Here G is countable while S is uncountable.
For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.
For each element a of a group G, conjugation by a is the operation φ < sub > a </ sub >: GG given by ( or a < sup >− 1 </ sup > ga ; usage varies ).

is and finitely
One example is the Banach – Tarski paradox which says that it is possible to decompose (" carve up ") the 3-dimensional solid unit ball into finitely many pieces and, using only rotations and translations, reassemble the pieces into two solid balls each with the same volume as the original.
" Almost all " is sometimes used synonymously with " all but finitely many " ( formally, a cofinite set ) or " all but a countable set " ( formally, a cocountable set ); see almost.
Clearly there is always at least one such string for any n, as otherwise all possible strings ( infinitely many ) could be generated by the ( finitely many ) programs with lower complexity, so GenerateComplexString must always return.
Specifically, a topological space is compact if, whenever a collection of open sets covers the space, some subcollection consisting only of finitely many open sets also covers the space.
Slightly more generally, any space with a finite topology ( only finitely many open sets ) is compact ; this includes in particular the trivial topology.
A theory about some topic is usually first-order logic together with: a specified domain of discourse over which the quantified variables range, finitely many functions which map from that domain into it, finitely many predicates defined on that domain, and a recursive set of axioms which are believed to hold for those things.
In mathematics, specifically commutative algebra, Hilbert's basis theorem states that every ideal in the ring of multivariate polynomials over a Noetherian ring is finitely generated.
Since is left-Noetherian, we have that must be finitely generated ; and since the comprise an-basis, it follows that for a finite amount of them, say < math >
* A ring is von Neumann regular if and only if every finitely generated right ( or every finitely generated left ) ideal is generated by an idempotent.
Hilbert's example: " the assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 ); and Brouwer's: " Every mathematical species is either finite or infinite.
If there is a finite generator of M, then M is said to be finitely generated.
This measure space is not σ-finite, because every set with finite measure contains only finitely many points, and it would take uncountably many such sets to cover the entire real line.
The oracle machine is initialized with the work tape containing some input with finitely many 1's and the rest of the tape blank, the oracle tape containing the characteristic function of the oracle, A, and the Turing machine in state q < sub > 0 </ sub > with read / write head reading the first nonblank cell of the work tape, and oracle head reading the cell of the oracle tape which corresponds to.
The universe is only finitely old, and stars have existed only for part of that time.
In this definition, a polytope is the union of finitely many simplices, with the additional property that, for any two simplices that have a nonempty intersection, their intersection is a vertex, edge, or higher dimensional face of the two.
Since the axioms in the schema in ( 5 ) cannot be replaced by any finite number of axioms, Presburger arithmetic is not finitely axiomatizable.
This topology differs from another, perhaps more obvious, topology called the box topology, which can also be given to a product space and which agrees with the product topology when the product is over only finitely many spaces.
The open sets in the product topology are unions ( finite or infinite ) of sets of the form, where each U < sub > i </ sub > is open in X < sub > i </ sub > and U < sub > i </ sub > ≠ X < sub > i </ sub > only finitely many times.

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