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

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.

Then is a derivation and is linear, i. e., and, and a Lie algebra homomorphism, i. e.,, but it is not always an algebra homomorphism, i. e. the identity does not hold in general.

Then the first argument becomes conjugate linear, rather than the second.

Let X be a normed topological vector space over F, compatible with the absolute value in F. Then in X *, the topological dual space X of continuous F-valued linear functionals on X, all norm-closed balls are compact in the weak -* topology.

Then any vector in R < sup > 3 </ sup > is a linear combination of e < sub > 1 </ sub >, e < sub > 2 </ sub > and e < sub > 3 </ sub >.

Then express the seed ( the initial conditions of the LRS ) as a linear combination of the eigenbasis vectors:

Then standard methods can be used to solve the linear difference equation in.

Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.

Then the resultant perturbation can be written as a linear sum of the individual types of perturbations,

Then it transfers to the anilox roll ( or meter roll ) whose texture holds a specific amount of ink since it is covered with thousands of small wells or cups that enable it to meter ink to the printing plate in a uniform thickness evenly and quickly ( the number of cells per linear inch can vary according to the type of print job and the quality required ).

Then they became entirely geometric or linear with raised dots.

Using the natural isomorphism between and the space of linear transformations from V to V ,< ref name =" natural iso "> Let L ( V, V ) be the space of linear transformations from V to V. Then the natural map

Then the zero vector of this space can be expressed as a linear combination of no elements, which again is an empty sum.

Then any linear functional can be written in these coordinates as a sum of the form:

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

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

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 a linear map is called a symplectic map if the pullback preserves the symplectic form, i. e., where the pullback form is defined by.

Then, L < sub > 0 </ sub > is a Lie algebra, L < sub > 1 </ sub > is a linear representation of L < sub > 0 </ sub >, and there exists a symmetric L < sub > 0 </ sub >- equivariant linear map such that for all x, y and z in L < sub > 1 </ sub >,

Let e < sub > i </ sub > denote the trivial path at vertex i. Then we can associate to the vertex i, the projective KΓ module KΓe < sub > i </ sub > consisting of linear combinations of paths which have starting vertex i. This corresponds to the representation of Γ obtained by putting a copy of K at each vertex which lies on a path starting at i and 0 on each other vertex.