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Page "Bijective proof" ¶ 4
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More and abstractly
More abstractly, one talks about the product in category theory, which formalizes these notions.
More abstractly, Campbell's idea that myths are how we shape our lives deeply informs the picture of life in Glorantha throughout the game world's publication history.
More abstractly, the convex-hull operator Conv () has the characteristic properties of a closure operator:
More abstractly, one can define the dicyclic group Dic < sub > n </ sub > as any group having the presentation
More abstractly, when using infix notation
More abstractly, the symplectic group can be defined as the set of linear transformations of a 2n-dimensional vector space over F that preserve a nondegenerate, skew-symmetric, bilinear form.
More abstractly, in classical mechanics phase space is the cotangent space of configuration space, and in this interpretaton the procedure above expresses that a choice of local coordinates on configuration space induces a choice of natural local Darboux coordinates for the standard symplectic structure on a cotangent space.
More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.
More abstractly, the integral can be written as the cap product of the homology class of Z and the cohomology class represented by α.
More abstractly, it can be defined as an incidence structure ( P, L, I ) consisting of a set P of points, a set L of lines, and an incidence relation I stating which points lie on which lines.
More generally and abstractly, given any group G and a representation of G on a vector space V,
More abstractly, it means that the cohomology class in the classifying space for pulls back from the cohomology class in under the inclusion ( which corresponds to the inclusion and similar ).
so too is the dual group More abstractly, these are both examples of representable functors, being represented respectively by K and T.
The order of PSL ( n, q ) is the above, divided by, the number of scalar matrices with determinant 1 – or equivalently dividing by, the number of classes of element that have no nth root, or equivalently, dividing by the number of nth roots of unity in .< ref group =" note "> These are equal because they are the kernel and cokernel of the endomorphism formally, More abstractly, the first realizes PSL as SL / SZ, while the second realizes PSL as the kernel of
More abstractly, a conservative vector field is an exact 1-form.
More generally, if W is a linear subspace of a ( possibly infinite dimensional ) vector space V then the codimension of W in V is the dimension ( possibly infinite ) of the quotient space V / W, which is more abstractly known as the cokernel of the inclusion.
More abstractly, it studies how global properties of a graph influence local substructures of the graph.
More abstractly, the mean curvature is the trace of the second fundamental form divided by n ( or equivalently, the shape operator ).
More abstractly, some aspects of the narrative appear in the crucifixion story of Jesus found in the gospels.
More abstractly: If X < sub > 1 </ sub >, ..., X < sub > n + 1 </ sub > are conditionally independent random variables that each can assume the value 0 or 1, then, if we know nothing more about them,
More abstractly, the " pay-off set " ( i. e., the set of all plays in which the angel wins ) is a closed set ( in the natural topology on the set of all plays ), and it is known that such games are determined.
More abstractly, f is proper if for any space Z the map
More abstractly, " G-bundles over X " is a functor in G: given a map H → G, one gets a map from H-bundles to G-bundles by inducing ( as above ).
More abstractly, a natural class of objects to study in topology are objects that are homogeneous ( all points are topologically the same: the group of self-homeomorphisms acts transitively ) and " finite type " or " tame " ( to rule out spaces such as the Cantor set, where each open set contains uncountably many connected components ); more generally, a space of " finite type " where the self-homeomorphism group has finitely many orbits, forming the strata.

More and generally
More generally, suppose that an experiment consists of a number of independent trials, that each trial results in either a `` success '' or a `` non-success '' ( `` failure '' ), and that the probability of success remains constant from trial to trial.
More generally, in a k-dimensional array, the address of an element with indices i < sub > 1 </ sub >, i < sub > 2 </ sub >, …, i < sub > k </ sub > is
More recently, an abettor is generally known as an accomplice.
More expensive pigments are generally replicated by hues.
More generally, one curve is a curvilinear asymptote of another ( as opposed to a linear asymptote ) if the distance between the two curves tends to zero as they tend to infinity, although usually the term asymptote by itself is reserved for linear asymptotes.
More generally, as noted by A. W.
More generally, a binary relation between two sets A and B is a subset of.
More generally, a new component is said to be backward compatible if it provides all of the functionality of the old component.
More generally, an n-piece cubic Bézier curve can approximate a circle, when each inner control point is the distance from an outer control point on a unit circle, where t is 360 / n degrees, and n > 2.
More generally, every C *- algebra is a Banach algebra.
More generally, a series
More generally, if ƒ has a branch-point near the origin of such a nature that then
More generally, calculus ( plural calculi ) refers to any method or system of calculation guided by the symbolic manipulation of expressions.
More generally, many philosophers and scientists have been unhappy about the difficulty of producing a definition that does not involve circularity or fuzziness.
More broadly, philosophers who do not accept the possibility of zombies generally believe that consciousness is reflected in behavior ( including verbal behavior ), and that we attribute consciousness on the basis of behavior.
Among the teachings of Jesus Christ in the Gospel of Luke and the Gospel of Matthew, the message to his followers that one should " Turn the other cheek " and his example in the story Pericope Adulterae, in which Jesus intervenes in the stoning of an adulteress, are generally accepted as his condemnation of physical retaliation ( though most scholars agree that the latter passage was " certainly not part of the original text of St John's Gospel ") More militant Christians consider Romans 13: 3 – 4 to support the death penalty.
* More generally, compact groups such as an orthogonal group are compact, while groups such as a general linear group are not.
More generally, compact sets can be separated by open sets: if K < sub > 1 </ sub > and K < sub > 2 </ sub > are compact and disjoint, there exist disjoint open sets U < sub > 1 </ sub > and U < sub > 2 </ sub > such that and.
More generally, electric current can be represented as the rate at which charge flows through a given surface as:
More generally, the idea of a contractive mapping can be defined for maps between metric spaces.
More generally, unspecific coercion may be the form taken by disciplinary coercion, and this appears to be in fact the case within the most effective command systems of the modern world.
More generally, judges look at the difficulty and execution of jumps, stunts and tumbling, synchronization, creativity, the sharpness of the motions, showmanship, and overall routine execution.
More generally among Baptists, a variety of parachurch agencies and evangelical educational institutions may be supported generously or not at all, depending entirely upon the local congregation's customs and predilections.
More generally, one can consider finite direct sums of matrix algebras.
More generally, inheritance now is quite different than those in the past.

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