For the answer cannot be derived from any socially cohesive element in the disrupting community.

For the truth formerly experienced by the community no longer has existential status in the community, nor does any answer elaborated by philosophers or theoriticians.

William Wimsatt and Cleanth Brooks, it seems to me, have a penetrating insight into the way in which this control is effected: `` For if we say poetry is to talk of beauty and love ( and yet not aim at exciting erotic emotion or even an emotion of Platonic esteem ) and if it is to talk of anger and murder ( and yet not aim at arousing anger and indignation ) -- then it may be that the poetic way of dealing with these emotions will not be any kind of intensification, compounding, or magnification, or any direct assault upon the affections at all.

For if Serenissimus made the sign of the Cross with his right hand, and meant it, with his left he beckoned lewdly to any lady who happened to catch his eye.

For them only a little more needed to be learned, and then all physical knowledge could be neatly sorted, packaged and put in the inventory to be drawn on for the solution of any human problem.

For one thing, there wasn't going to be any ceremony at all this year.

For that reason any democratic reform and effort to bring genuine representative government to the Dominican Republic will need the greatest sympathy and help.

For those communities which have financial difficulties in effecting adjustments, there are a number of alternatives any one of which alone, or in combination with others, would minimize if not even eliminate the problem.

For United States expenditures under subsections ( A ), ( B ), ( D ), ( E ), ( F ), ( H ) through ( R ) of Section 104 of the Act or under any of such subsections, the rupee equivalent of $200 million.

For the making of selections on the basis of excellence requires that any foundation making the selections shall have available the judgments of a corps of advisors whose judgments are known to be good: such judgments can be known to be good only by the records of those selected, by records made subsequent to their selection over considerable periods of time.

For the near term, however, it must be realized that the industrial and commercial market is somewhat more sensitive to general business conditions than is the military market, and for this reason I would expect that any gain in 1961 may be somewhat smaller than those of recent years ; ;

For any house.

For proper accreditation of schools, teachers in any course must have a degree at least one level above that for which the student is a candidate.

For any such square the middle corner of these will be called the vertex of the square and the corner not on the curve will be called the diagonal point of the square.

For the lines of any plane, **yp, meeting Q in a conic C, are transformed into the congruence of secants of the curve C' into which C is transformed in the point involution on Q.

For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.

For any choice of admissible policy Af in the first stage, the state of the stream leaving this stage is given by Af.

For in the modern world neither `` spirit '' nor `` matter '' refer to any generally agreed-upon elements of experience.

For in Christ Jesus neither circumcision nor uncircumcision but a new creation is of any account.

For example for any ( even infinite ) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection, but for an infinite collection of pairs of socks ( assumed to have no distinguishing features ), such a selection can be obtained only by invoking the axiom of choice.

: For any set X of nonempty sets, there exists a choice function f defined on X.

: For any set A, the power set of A ( with the empty set removed ) has a choice function.

: For any set A there is a function f such that for any non-empty subset B of A, f ( B ) lies in B.

For more information, consult the Wikipedia article on affine transformations.

For example, if the affine transformation acts on the plane and if the determinant of A is 1 or − 1 then the transformation is an equi-areal mapping.

For more complex recognition problems, intelligent character recognition systems are generally used, as artificial neural networks can be made indifferent to both affine and non-linear transformations.

For example, is a meromorphic function on the two-dimensional complex affine space.

For other values of this falls in the more general class of affine maps.

For example, the three dimensional Euclidean space is not a countable union of its affine planes.

For example, the theorem from the plane geometry of triangles about the concurrence of the lines joining each vertex to the midpoint of the opposite side ( at the centroid or barycenter ) depends on the notions of mid-point and centroid as affine invariants.

For that reason a concept of affine algebraic group is redundant over a field — we may as well use a very concrete definition.

For any affine algebraic set V, the coordinate ring or structure ring of V is the quotient of the polynomial ring by this ideal.

For the function field even to be defined, V here must be an irreducible algebraic set ; in which case the function field ( for an affine variety ) is just the field of fractions of the coordinate ring of V. Using polynomial equations, it is easy to define sets that have ' mixed dimension ': a union of a curve and a plane in space, for example.

If, for example, we simply look at a curve in the real affine plane there might be singular P modulo the stalk, or alternatively as the sum of m ( m − 1 )/ 2, where m is the multiplicity, over all infinitely near singular points Q lying over the singular point P. Intuitively, a singular point with delta invariant δ concentrates δ ordinary double points at P. For an irreducible and reduced curve and a point P we can define δ algebraically as the length of where is the local ring at P and is its integral closure.

For affine buildings, this metric satisfies the CAT ( 0 ) comparison inequality of Alexandrov, known in this setting as the Bruhat-Tits non-positive curvature condition for geodesic triangles: the distance from a vertex to the midpoint of the opposite side is no greater than the distance in the corresponding Euclidean triangle with the same side-lengths ( see ).

For the affine group, an apartment is just the simplicial complex obtained from the standard tessellation of Euclidean space E < sup > n-1 </ sup > by equilateral ( n-1 )- simplices ; while for a spherical building it is the finite simplicial complex

For example, in, the origin, lines and planes through the origin and the whole space are linear subspaces, while points, lines and planes in general as well as the whole space are the affine subspaces.

For example, the affine span of a set of two points is the line that contains both ; the affine span of a set of three non-collinear points is the plane that contains all three.

For instance, Möbius transformations ( transformations of the complex projective line, or Riemann sphere ) are affine ( transformations of the complex plane ) if and only if they fix the point at infinity.

For instance, an affine connection, the most elementary type of connection, gives a means for transporting tangent vectors to a manifold from one point to another along a curve.

Morphisms from schemes to affine schemes are completely understood in terms of ring homomorphisms by the following contravariant adjoint pair: For every scheme X and every commutative ring A we have a natural equivalence

For example, a circle is a concept that makes sense in Euclidean geometry, but not in affine linear geometry or projective geometry, where circles cannot be distinguished from ellipses, since one may squeeze a circle to an ellipse.

For example, given the four points the pencil of conics through them can be parameterized as yielding the following pencil ; in all cases the center is at the origin :< ref group =" note "> A simpler parametrization is given by which are the affine combinations of the equations and corresponding the parallel vertical lines and horizontal lines, and results in the degenerate conics falling at the standard points of

For example, the left and right invariant Haar measures on the affine group are not equal.

For 2D space and affine transform the basis is defined by a pair of points.

For the mentioned-families the affine connection is called the-connection and can also be expressed in more ways.