Then, I remembered that the girls had had a banana for dessert every day for the last week.

Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.

Then every component of the graph of F must be defined over a bounded sub-interval.

Then our choice function can choose the least element of every set under our unusual ordering.

After this, the senior priest ( or bishop ) pours pure olive oil and a small amount of wine into the shrine lamp, and says the " Prayer of the Oil ", which calls upon God to "... sanctify this Oil, that it may be effectual for those who shall be anointed therewith, unto healing, and unto relief from every passion, every malady of the flesh and of the spirit, and every ill ..." Then follow seven series of epistles, gospels, long prayers, Ektenias ( litanies ) and anointings.

Then, since every real is the limit of some Cauchy sequence of rationals, the completeness of the norm extends the linearity to the whole real line.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Then almost every point of A returns to A infinitely often.

Then I got the script and my name was on every page because it was about my car.

In every medium, spy thrillers introduce children and adolescents to deception and espionage at earlier ages, as in the Agent Cody Banks film, the Alex Rider adventure novels by Anthony Horowitz, chick lit novels such as I'd Tell You I Love You, But Then I'd Have to Kill You and the CHERUB series, by Robert Muchamore.

Then the equivalence class of the identity is the symmetry group of the figure, and every equivalence class corresponds to one isomorphic version of the figure.

Those who believe and those who are Jews and Christians, and Sabians, whoever believes in Allah and the Last Day and do righteous good deeds shall have their reward with their Lord, on them shall be no fear, nor shall they grieve ... let there be no compulsion in religion "-that all monotheistic religions or people of the book have a chance of salvation, to the most exclusive teaching common amongst Salafis and Wahhabis, and supported by several works of medieval Islamic theology and by traditions ( hadith ) which are considered correct ( sahih ) by Sunni Muslims, for the most part are summed up in Surah 9: 5, 29: " Then, when the sacred months have passed, slay the idolaters wherever ye find them, and take them, and besiege them, and lay in wait in every stratagem of war.

Then every subset of X is either considered " almost everything " ( has measure 1 ) or " almost nothing " ( has measure 0 ).

It looked to me as if the whole town would break out into a riot ... Then suddenly I heard a heavy thump, and as if by magic the whole crowd dispersed in every direction ... One of the regular patrons had felled one of the noisiest rioters .... And it was the effect of this which had scattered everybody so suddenly.

Then I shall crucify you every one.

Then he ordered 2 golden pieces to be given to every householder in Constantinople and 200 pounds of gold ( including 200 silver pieces annually ) to be given to the Byzantine Church.

Then a fuzzy subset s: S of a set S is recursively enumerable if a recursive map h: S × N Ü exists such that, for every x in S, the function h ( x, n ) is increasing with respect to n and s ( x ) = lim h ( x, n ).

Suppose a partially ordered set P has the property that every chain ( i. e. totally ordered subset ) has an upper bound in P. Then the set P contains at least one maximal element.

Suppose a non-empty partially ordered set P has the property that every non-empty chain has an upper bound in P. Then the set P contains at least one maximal element.

Then, when the clock reaches midnight, there will be firework at Taipei 101 and every year since, the firework has last longer than the year before.

Then, still black with smoke and with his uniform in shreds, Nelson went on board Victory where he was received on the quarter-deck by Admiral Jervis – " the Admiral embraced me, said he could not sufficiently thank me, and used every kind expression which could not fail to make me happy.

Then is an open cover of S, but any finite subcollection of has the form of C discussed previously, and thus cannot be an open subcover of S. This contradicts the compactness of S. Hence, every accumulation point of S is in S, so S is closed.

Then every hom-set has an addition, endowing it with the structure of an abelian monoid, and such that the composition of morphisms is bilinear.

Let X be a compact complex manifold of complex dimension n. Then X is an orientable smooth manifold of real dimension 2n, so its cohomology groups lie in degrees zero through 2n.

Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

Then every non-torsion cohomology class in H < sup > 2k </ sup >( X, Z ) ∩ H < sup > k, k </ sup >( X ) is the cohomology class of an algebraic cycle with integral coefficients on X.

Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

Then the topological cohomology of X does not change, but the Hodge decomposition does change.

Then the only nontrivial Chern class is the first Chern class, which is an element of the second cohomology group of X.

Then the cohomology of X can be computed from that of the projective space:

If we take E to be the sum of the even exterior powers of the cotangent bundle, and F to be the sum of the odd powers, define D = d + d *, considered as a map from E to F. Then the topological index of D is the Euler characteristic of the Hodge cohomology of M, and the analytical index is the Euler class of the manifold.

Then the ith cohomology group is just the coherent cohomology group H < sup > i </ sup >( X, V ), so the analytical index of this complex is the holomorphic Euler characteristic Σ (− 1 )< sup > i </ sup > dim ( H < sup > i </ sup >( X, V )).

Then sheaf cohomology enables us to consider a similar extension problem while " continuously varying " the Abelian group.

Denote this Thom class by U. Then for a class b in the cohomology of the base, we can compute the Thom isomorphism via the pullback of the bundle projection and the cohomology cup product:

Then epistolatory me was a foreign correspondent dispatching exciting cables and communiques, full of dash and wit and glamor, quoting from the books I read, imitating the grand styles of the authors recommended by a teacher in whose special, after-school class I was enrolled.

Then all elements of X equivalent to each other are also elements of the same equivalence class.

Then the equivalence class of the pair can be identified with the rational number, and this equivalence relation and its equivalence classes can be used to give a formal definition of the set of rational numbers.

Then, once this claim ( expressed in the previous sentence ) is proved, it will suffice to prove " φ is either refutable or satisfiable " only for φ's belonging to the class C. Note also that if φ is provably equivalent to ψ ( i. e., ( φ ≡ ψ ) is provable ), then it is indeed the case that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable " ( the soundness theorem is needed to show this ).

⟨ H ⟩, be the group generated by H. Then the word problem in H < sup >*</ sup > is solvable: given two words h, k in the generators H of H < sup >*</ sup >, write them as words in X and compare them using the solution to the word problem in G. It is easy to think that this demonstrates a uniform solution the word problem for the class K ( say ) of finitely generated groups that can be embedded in G. If this were the case the non-existence of a universal solvable word problem group would follow easily from Boone-Rogers.

Then, in 1960, Pope John XXIII issued the Code of Rubrics, completely ending the ranking of feast days by doubles etc., and replacing it by a ranking, applied not only to feast days but to all liturgical days, as I, II, III, and IV class days.

Let be the mean of the values in associated with class c, and let be the variance of the values in associated with class c. Then, the probability of some value given a class,, can be computed by plugging into the equation for a Normal distribution parameterized by and.

The other class of Dedekind rings which is arguably of equal importance comes from geometry: let C be a nonsingular geometrically integral affine algebraic curve over a field k. Then the coordinate ring k of regular functions on C is a Dedekind domain.

Then, viral glycoprotein gp42 interacts with cellular MHC class II molecules.

Then a new datum is associated with the class such that it's best sparsely represented by the corresponding dictionary.

Then every Hodge class on X is algebraic.

Then every Hodge class on X is a linear combination with rational coefficients of Chern classes of vector bundles on X.

Then every Hodge class on X is a linear combination with rational coefficients of Chern classes of coherent sheaves on X.

Then, there was feudal society, in which lord and serf played the roles of class war.

Then he went to the Chandragiri government high school, till class 9.