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Page "Theory of computation" ¶ 11
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We and thus
We may thus trace the notion of individual autonomy from its manifestation in religious practice and theological reflection through practical politics and political theory into literature and the arts.
In the rhyming catechism this doctrine is worded thus: `` In Adam's fall We sin-ned all ''.
We have chosen to give it at the end of the section since it deals with differential equations and thus is not purely linear algebra.
We thus have an optimal policy which maximizes the expected value of the objective function for a given Af.
We will make a few simplifying assumptions: that the uncompressed volume of the cylinder is 1000cc's ( one liter ), that the gas within is nearly pure nitrogen ( thus a diatomic gas with five degrees of freedom and so
We know that is opaque and thus follows that is opaque, so in the above equation, each operator can be written as a convex combination:
Leary received an honorary doctorate and spoke briefly at his alma mater's undergraduate commencement ceremony on May 16, 2005 ; he is thus credited as " Dr. Denis Leary " on the cover of his 2009 book, Why We Suck.
We have explained that ' regularity ' must be understood to exclude all pseudo-initiatic organizations, which, regardless of pretention and outward appearance, in no way possess any spiritual influence and thus are incapable of transmitting anything .”
The EPR paper says: " We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.
Here, we are told, ' We need to go beyond the pleasure principle, the reality principle, and repetition compulsion to ... the fantasy principle ' - ' not, as Freud did, reduce fantasies to wishes ... consider all other imaginable emotions '; and thus envisage emotional fantasies as a possible means of moving beyond stereotypes to more nuanced forms of personal and social relating.
We thus obtain a functor from the category of pointed topological spaces to the category of groups.
We have thus over-counted the actual number of states.
We thus say that dog and dogs are different forms of the same lexeme.
In response to the claim in Whewell's treatise that " We may thus, with the greatest propriety, deny to the mechanical philosophers and mathematicians of recent times any authority with regard to their views of the administration of the universe ", Charles Babbage published what he called The Ninth Bridgewater Treatise, A Fragment.
We sent it in, and Schopf reacted strongly against it — thus signaling the tenor of the reaction it has engendered, though for shifting reasons, down to the present day.
We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.
We thus obtain the inequality in terms of dimensions of kernel, which can then be converted to the inequality in terms of ranks by the rank-nullity theorem.
We are enabled thus to contrast Tacitus with Josephus, who warped his narrative to do honour to Titus.
We can thus understand the high importance of barriers, whether of land or water, which separate our several zoological and botanical provinces.
We can thus understand the localisation of sub-genera, genera, and families ; and how it is that under different latitudes, for instance in South America, the inhabitants of the plains and mountains, of the forests, marshes, and deserts, are in so mysterious a manner linked together by affinity, and are likewise linked to the extinct beings which formerly inhabited the same continent ... On these same principles, we can understand, as I have endeavoured to show, why oceanic islands should have few inhabitants, but of these a great number should be endemic or peculiar ; ...
i. e., z is a vector orthogonal to the vector v ( Indeed, z is the projection of u onto the plane orthogonal to v .) We can thus apply the Pythagorean theorem to
We obtain the same variation in probability amplitudes by allowing the time at which the photon left the source to be indeterminate, and the time of the path now tells us when the photon would have left the source, and thus what the angle of its " arrow " would be.
We recognize this genre ; thus, expectations are set.
We have also come to understand Harvey's somewhat unorthodox method of dealing with his gout, here cited completely: "... his ( Harvey's ) cure was thus: he would sit with his legs bare ... put them into a pail of water till he was almost dead with cold, then betake himself to his stove, and so ' twas gone ".

We and say
`` We think the governor treated us rather shabbily, to say the least of it.
We often say of a person that he `` looks young for his age '' or `` old for his age ''.
We may say of some unfortunates that they were never young.
We cannot truthfully say of anyone who has succeeded in entering deep into his sixties that he was never old.
We sympathize with Mr. Kennedy, but we feel bound to say that his budget review doesn't please us either, although for very different reasons.
We couldn't be seen together, for the tongue of Scandal was ever ready to link our names, and the tongue of Scandal finds but one thing to say of the association of a man with a girl, no matter how innocent.
We say that N is nilpotent if there is some positive integer R such that Af.
We may say that his problem was diagnosed but that he refused treatment.
We may say that his attitude was foolish, since he may have been a success had he learned some human relations skills ; ;
We should say that we made our point with feeling the first time and little or no feeling the second time, but that it was the same point we were making.
We may carry this sequence one step further and say that at seventy he was a poet at the height of his powers, wanting only the impetus of two tragedies, one personal, the other national, to loose those powers in poetry.
`` We worry '', say the mothers.
We have to tell ourselves that when Parker spoke in this vein, he believed what he said, because he could continue, `` But the truth, which cost me bitter tears to say, I must speak, though it cost other tears hotter than fire ''.
We do not say that a man who takes no interest in politics is a man who minds his own business ; we say that he has no business here at all.
We say A is unital if it contains an element 1 such that
We can say that that relation has being as well.
We say we want to see put on the statute book something which will make our people citizens of the world before they are citizens of this country ".
We might not see any rotation initially, but if we closely look at the right, we see a larger field at, say, x = 4 than at x = 3.
We say that the mutation is recessive because the organism will exhibit the wild type phenotype ( ordinary trait ) unless both chromosomes of a pair have the mutation ( homozygous mutation ).
We say that f is a diffeomorphism if it is bijective, smooth, and if its inverse is smooth.
We can distort a dual polyhedron such that it can no longer be obtained by reciprocating the original in any sphere ; in this case we can say that the two polyhedra are still topologically dual.
We have to also say how to add their elements.
We can use it as basis to say, " a < b " and " b > a ", two judgments which designate the same state of affairs.
: “ We say that it origin of the traditions is polar, and the pole is nomore Western than it is Eastern.

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