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 example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers.

For example, a smooth manifold is a Hausdorff topological space that is locally diffeomorphic to Euclidean space.

For example, a homomorphism of topological groups is often required to be continuous.

For a topological space X, the following are equivalent:

For example, a bijective linear map is an isomorphism between vector spaces, and a bijective continuous function whose inverse is also continuous is an isomorphism between topological spaces, called a homeomorphism.

For measure spaces that are also topological spaces various compatibility conditions can be placed for the measure and the topology.

For any topological space X, let C ( X ) denote the family of real-valued continuous functions on X and let C *( X ) be the subset of bounded real-valued continuous functions.

For instance, the general linear group GL ( n, R ) of all invertible n-by-n matrices with real entries can be viewed as a topological group with the topology defined by viewing GL ( n, R ) as a subset of Euclidean space R < sup > n × n </ sup >.

For example, in any topological group the identity component ( i. e. the connected component containing the identity element ) is a closed normal subgroup.

For a topological space X, the collection of all Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra.

For example, a topological group is just a group in the category of topological spaces.

For a given space X, the existence of an embedding X → Y is a topological invariant of X.

For general topological spaces X, the map from X to βX need not be injective.

For example, in the category of topological abelian groups, the image of a morphism actually corresponds to the inclusion of the closure of the range of the function.

For example, a path-connected topological space is simply connected if each loop ( path from a point to itself ) in it is contractible ; that is, intuitively, if there is essentially only one way to get from any point to any other point.

For example, a topological space is totally disconnected if each of its components is a single point.

For this discussion, the universe is taken to be a geodesic manifold, free of topological defects ; relaxing either of these complicates the analysis considerably.

For example, the quantum finite automaton or topological automaton has uncountable infinity of states.

For a topological space, the homology groups are generally much easier to compute than the homotopy groups, and consequently one usually will have an easier time working with homology to aid in the classification of spaces.

For a surface which is the topological boundary of a set in three dimensions, one can distinguish between the inward-pointing normal and outer-pointing normal, which can help define the normal in a unique way.

For a topological space X, the cohomology group H < sup > n </ sup >( X ; G ), with coefficients in G, is defined to be the quotient Ker ( δ < sup > n </ sup >)/ Im ( δ < sup > n-1 </ sup >) at C < sup > n </ sup >( X ; G ) in the cochain complex

For example, it is possible to find shortest paths and longest paths from a given starting vertex in DAGs in linear time by processing the vertices in a topological order, and calculating the path length for each vertex to be the minimum or maximum length obtained via any of its incoming edges.

For example, in the topological space ω < sub > 1 </ sub >+ 1, the element ω < sub > 1 </ sub > is in the closure of the subset ω < sub > 1 </ sub > even though no sequence of elements in ω < sub > 1 </ sub > has the element ω < sub > 1 </ sub > as its limit: an element in ω < sub > 1 </ sub > is a countable set ; for any sequence of such sets, the union of these sets is the union of countably many countable sets, so still countable ; this union is an upper bound of the elements of the sequence, and therefore of the limit of the sequence, if it has one.