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Page "Euler's criterion" ¶ 15
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So and every
So much had he become the rage that every rich woman who had mislaid a bracelet or lost a pet kitten rushed to secure the services of the great Hercule Poirot.
So to classify these groups one takes every central extension of every known finite simple group, and finds all simple groups with a centralizer of involution with this as a component.
) So far, observations show any rotation of the Universe is very slow ( no faster than once every 60 · 10 < sup > 12 </ sup > years ( 10 < sup >− 13 </ sup > rad / yr )), and debate persists over whether there is any rotation.
So in particular, every central idempotent a in R gives rise to a decomposition of R as a direct sum of the corner rings aRa and.
So every abstract Lie algebra is the Lie algebra of some ( linear ) Lie group.
So long as everyone was using the same tactics these weaknesses were not immediately apparent, but with the advent of the Roman legion they proved fatal in every major engagement, the most famous being the Battle of Pydna, as the Romans were able to advance through gaps in the line and easily defeat the phalangites once in close.
So, for example, every second-countable manifold is metrizable.
So for example, for these authors, it is true of every set A that A ⊂ A.
So she pored over every book on mathematics in her father's library, even teaching herself Latin and Greek so she could read works like those of Sir Isaac Newton and Leonhard Euler.
So every time a message is sent to these instances they actually get sent, hence they intercede in the message sending process.
So every country decides on its own which road to take.
" So, while " each and every law must be rooted in either the Qur ' an or the Sunnah ," without contradiction, tribal life brought about a sense of participation.
So a ToE must work for a wide range of simple examples in such a way that we can be reasonably confident it will work for every situation in physics.
So much sediment is carried by the Mekong's various branches and tributaries that the delta advances sixty to eighty meters into the sea every year.
So path-ascending crawler was introduced that would ascend to every path in each URL that it intends to crawl.
So, out of every 16 nucleons ( 2 neutrons and 14 protons ), 4 of these ( 25 % of the total particles and total mass ) combine quickly, once temperatures are lowered, into one helium-4 nucleus.
So, at every moment of time there exists not only a wave function, but also a well-defined configuration of the whole universe.
Moreover Bacchylides's line " So now for me too countless paths extend in all directions " has a close resemblance to lines in one of Pindar's Isthmian Odes ( 1. 1 – 2 ), " A thousand ways ... open on every side widespread before me " but, as the date of Pindar's Isthmian Ode is uncertain, it is not clear in this case who was imitating whom.
Romulus kills him, saying " So perish every one that shall hereafter leap over my wall ".
He wrote in 1939, “ So much of every art is an expression of the subconscious that it seems to me most of all the important qualities are put there unconsciously, and little of importance by the conscious intellect .”
So the conditions of an eclipse are met when the new or full moon is near one of the nodes, which occurs every 5 or 6 months ( the Sun, being in conjunction or opposition to the Moon, is also at a node of the Moon's orbit at that time-this happens twice in an eclipse year ).
:" So, distinguishing the whole people by the several arts and trades, he formed the companies of musicians, goldsmiths, carpenters, dyers, shoemakers, skinners, braziers, and potters ; and all other handicraftsmen he composed and reduced into a single company, appointing every one their proper courts, councils, and observances.
So far, the neighboring jurisdictions have diminished Gumlog at every opportunity.

So and quadratic
So in particular it has a natural positive definite quadratic form, and the corresponding completion is a Hilbert space A ⊗ B, called the ( Hilbert space ) tensor product of A and B.

So and residue
So in this case too, the distillate moves away from the azeotrope and the residue moves toward it.
So a nonzero number is a residue mod 8, 16, etc., if and only if it is of the form 4 < sup > k </ sup >( 8n + 1 ).
So these primes have residue degree 2, so they split into exactly three prime ideals in a degree 6 extension of Q with it as Galois group.
So when legume residue decomposes, soil microbes have sufficient N available to enhance their breakdown of organic materials in the soil.

So and mod
So Euler's theorem yields 7 < sup > 4 </ sup > ≡ 1 ( mod 10 ), and we get 7 < sup > 222 </ sup > ≡ 7 < sup > 4 × 55 + 2 </ sup > ≡ ( 7 < sup > 4 </ sup >)< sup > 55 </ sup >× 7 < sup > 2 </ sup > ≡ 1 < sup > 55 </ sup >× 7 < sup > 2 </ sup > ≡ 49 ≡ 9 ( mod 10 ).
So the multiplicative order of 11 ( mod 71 ) is 70, and thus 71 is prime.
So the formula evaluates as ( 1 + 36 + 99 + 24 + 4 − 38 ) mod 7

So and p
So we can conclude that the original proposition, ¬ p, must be true — " there is no smallest rational number greater than 0 ".
So too with " g " and " c ", and " p " and " b ", and also " s " and " z " ( and " x ").
So the length of a curve γ from p to q is a functional of the curve given by
So, it was argued, the Mediterranean had once opened a passage for itself by the Columns of Hercules into the Atlantic, and perhaps the abundance of sea-shells in Africa, near the Temple of Jupiter Ammon, might also be the deposit of some former inland sea, which had at length forced a passage and escaped .</ p >
So, p and q are Euclidean vectors, starting from the origin of the space, and their tips indicate two points.
So p ( 4 ) = 5.
So, to prove ( 1 ), assume that m and p are surjective and q is injective.
So we calculate the greatest common divisor of the polynomials p ( x ) and p ′( x ); adjust the leading coefficient to be one and call it g ( x ).
So the multiple root of p ( x ) is r = 1.
So, third nature is able to ‘ speed up, proliferate, divide, mutate, and beam in on us from else where ( Wark, 1997, p. 25 ).
774, at p. 824, Lord Mansfield disparaged the practice of jury nullification: So the jury who usurp the judicature of law, though they happen to be right, are themselves wrong, because they are right by chance only, and have not taken the constitutional way of deciding the question.
So whatever community it may be, it is necessary for it to have this kind of spiritual support .</ p >
So the manifold T * M itself carries local coordinates ( x < sup > i </ sup >, p < sub > i </ sub >) where the x are coordinates on the base and the p are coordinates in the fibre.
where the derivatives are taken at the point p. So they are
< p > So every evening she stole back and slept in his arms .</ p >
So there is one pair of poles per phase, which means p
Friedan stated in her memoir Life So Far ( 2000 ) that Carl had beaten her during their marriage ; friends such as Dolores Alexander recalled having to cover up black eyes from Carl's abuse in time for press conferences ( Brownmiller 1999, p. 70 ).
Crossfade had their first radio appearance (" So Far Away ") heard on 94. 5 the Buzz ( Houston, Texas ) Cage Match at 10 o ' clock p. m. where it competed with a new song every night and won out over the competition for over three weeks.
* Tonello, Fabrizio ( 2007 ) Così negli Usa è fallita la Tolleranza zero So Zero Tolerance failed in the US published by il manifesto 31 August 2007, p. 5
So given the lengths p, q, r and s of a cyclic quadrilateral, the approximate area is while, letting, the exact area is
So we have, Q < sub > p </ sub > =

2.949 seconds.