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Page "Fundamental group" ¶ 27
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turns and out
They may even enroll a colored student or two for show, though he usually turns out to be from Thailand, or any place other than the American South.
but when the bird is found at last, it turns out to be a fake.
Precisely at the moment when it has lost its vision the mind of the community turns out from itself in a search for the ontological standard whereby it can measure itself.
As Yinger has pointed out, the `` reliance on symbols, on tradition, on sacred writings, on the cultivation of emotional feelings of identity and harmony with sacred values, turns one to the past far more than to the future ''.
The result of this attitude has been the domination of many orthography conferences by such considerations as typographic ' esthetics ', which usually turns out to be nothing more than certain prejudices carried over from European languages.
The actual surface becomes both ground and background, and it turns out -- suddenly and paradoxically -- that the only place left for a three-dimensional illusion is in front of, upon, the surface.
`` The trouble, '' explained Loy Henderson, then Deputy Undersecretary for Administration, `` is that when we get into an argument with him about this thing, it always turns out that Rooney knows more about our budget than we do ''.
Now, if Morton's newest product, a corn chip known as Chip-o's, turns out to sell as well as its stock did, the stock may turn out to be worth every cent of the prices that the avid buyers bid it up to.
The cleaner equipment firm began operations in 1953 and the unit system, which turns out a complete ginning system, began operations in 1959.
Actually, however, this turns out to be only part of the picture.
This is when his troubles begin, not to mention a fledgling artist who he hires, and who turns out to have ideas of his own, with particular respect to the hero's sweetheart-secretary.
What might have been only warmed-over topical journalism turns out to be an eyewitness contribution to history.
" The problem then becomes that of constructing a well-ordering, which turns out to require the axiom of choice for its existence ; every set can be well-ordered if and only if the axiom of choice holds.
Twice, the murderer surprisingly turns out to be the unreliable narrator of the story.
It turns out that a more suitable quantity for updating is the sum of squares of differences from the ( current ) mean,, here denoted:
Dürer's belief in the abilities of a single artist over inspiration prompted him to assert that " one man may sketch something with his pen on half a sheet of paper in one day, or may cut it into a tiny piece of wood with his little iron, and it turns out to be better and more artistic than another's work at which its author labours with the utmost diligence for a whole year.
The system of having two rectors was found to lead to frequent quarrels and the republic thenceforth sent out a single official styled Bailie and Captain, assisted by two councilors, who performed the duties of camerlengo by turns.
As it turns out, even the historians and expert researchers have been fooled and forced to reassess their conclusions over “ Cup ’ s ” paintings over the years.
For a system of point particles without any intrinsic angular momentum ( see below ), it turns out to be
Unfortunately, it turns out that Miles Gloriosus has just returned from Crete, where there is of course no actual plague.
The percentage of fluent speakers turns out to be even higher if those under 16 are also taken into account, given that the proportion of bilinguals is particularly high in this age group ( 76. 7 % of those aged between 10 and 14 and 72. 4 % of those aged 5 – 9 ): 37. 5 % of the population aged 6 and above in the whole Basque Autonomous Community, 25. 0 % in Álava, 31. 3 % in Biscay and 53. 3 % in Gipuzkoa.
Players on the batting team take turns hitting against the pitcher of the fielding team, which tries to stop them from scoring runs by getting hitters out in any of several ways.
It turned out that the Cubs and Giants ended the season tied for first place, so the game was indeed replayed, and the Cubs won the game, the pennant, and subsequently the World Series ( the last Cubs Series victory to date, as it turns out ).

turns and functor
A contravariant functor, is like a covariant functor, except that it " turns morphisms around " (" reverses all the arrows ").
Then it turns out that a functor between pre-abelian categories is left exact if and only if it is additive and preserves all kernels, and it's right exact if and only if it's additive and preserves all cokernels.
If is a set such that all products for families indexed with exist, then it is possible to choose the products in a compatible fashion so that the product turns into a functor.
More generally, the homology functor is defined axiomatically, as a functor on an abelian category, or, alternately, as a functor on chain complexes, satisfying axioms that require a boundary morphism that turns short exact sequences into long exact sequences.
But it turns out that ( if A is " nice " enough ) there is one canonical way of doing so, given by the right derived functors of F. For every i ≥ 1, there is a functor R < sup > i </ sup > F: A B, and the above sequence continues like so: 0 F ( A ) F ( B ) F ( C ) R < sup > 1 </ sup > F ( A ) R < sup > 1 </ sup > F ( B ) R < sup > 1 </ sup > F ( C ) R < sup > 2 </ sup > F ( A ) R < sup > 2 </ sup > F ( B ) ....
Alternatively, one can argue that every short exact sequence of k-vector spaces splits, and any additive functor turns split sequences into split sequences.
A covariant ( not necessarily additive ) functor is left exact if and only if it turns finite limits into limits ; a covariant functor is right exact if and only if it turns finite colimits into colimits ; a contravariant functor is left exact if and only if it turns finite colimits into limits ; a contravariant functor is right exact if and only if it turns finite limits into colimits.

turns and cannot
And in the new `` King Of Kings '' the plot involves intrigues and twists and turns that cannot be traced to the Gospels.
Although there is no obvious restriction that any given regular polygon cannot be a face of a Johnson solid, it turns out that the faces of Johnson solids always have 3, 4, 5, 6, 8, or 10 sides.
When the king turns over temporalities to the clergy, he places them under his jurisdiction, from which later pronouncements of the popes cannot release them.
However, in the 1930s Gödel's incompleteness theorems convinced many mathematicians that mathematics cannot be reduced to logic alone, and Karl Popper concluded that " most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently.
The permanent axis must turn towards this line, since the body cannot continue to rotate about any line that is not a principal axis of maximum moment of inertia ; that is, the permanent axis turns in a direction at right angles to that in which the torque might be expected to turn it.
And the geographer, as he turns over the folios, with their details of population and of arable, woodland, meadow and other resources, cannot but be excited at the vast amount of information that passes before his eyes.
I cannot remember in my entire life such a change in the attitude of a crowd in a few minutes, almost a few seconds ... Hitler had turned them inside out, as one turns a glove inside out, with a few sentences.
If blood can get in, but cannot get out because one of the veins has been blocked, that part of the body turns purple.
# A player cannot play a stone which results in a copy of the board two turns earlier.
When he refuses, as he still cannot stand the beverage after the events of the previous book, Castafiore turns into a huge bird-like creature and begins to attack Haddock.
As it turns out, subtle kinds of holes exist that homology cannot " see " — in which case homotopy groups may be what is needed.
She turns to witchcraft only in despair ; it cannot be taken as an unequivocal manifestation of diabolic power.
When Johnny turns himself in, he finds Buzz about to confess to Helen's murder, even though he cannot remember what happened that night.
Since Kubera's friend, Yama, is the obvious next target, Kubera tricks Sam, who has forgotten what a great warrior the fat old man was, and in a bout of Irish Stand-Down ( in which two men take turns hitting each other until one cannot continue ), knocks him out and prepares to flee on the giant bird Garuda.
Hallam responds with a furious effort and eventually finds that the sample, originally tungsten, has been transformed into something that turns out to be plutonium 186 — an isotope that cannot occur naturally in our universe.
She is forced to find the son of Time, whom Death cannot influence or even see, because — being only " mostly human "— the boy is not subject to death ( though it turns out he is also " mostly not " human ).
Hilfy rescues Atli-lyen-tlas, but discovers that gtst, due to the stress of gtst's ordeal and old age, has become gtsta, or neuter, and cannot accept the oji, which turns out to constitute a marriage proposal from No ' shto-shti-stlen.
However, it turns out there are languages that cannot be decided by push-down automaton either.
In 1999 he was awarded the Balzan Prize for Philosophy " For his capacity in bringing together all the most important themes and indications of 20th century philosophy, and re-elaborating them into an original synthesis which turns language-in particular, that which is poetic and metaphoric-into a chosen place revealing a reality that we cannot manipulate, but interpret in diverse ways, and yet all coherent.
Lanark begins to associate with a group of twenty-somethings to whom he cannot fully relate and whose mores he cannot understand, and soon begins to suffer from Dragonhide, a disease which turns his skin into scales as an external manifestation of his emotional repression.
Baseball and softball games cannot end until both teams have had an equal number of turns at bat, unless further play ( by the home team if they lead after 8 1 / 2 innings ) cannot affect the outcome.
Because the particles cannot exchange places, one might expect their behaviour to be fermionic, but it turns out that their behaviour differs from that of fermions in several important ways: the particles can all occupy the same momentum state which corresponds to neither Bose – Einstein nor Fermi – Dirac statistics.

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