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Page "Formal group" ¶ 62
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Conversely and given
Conversely, a current of one ampere is one coulomb of charge going past a given point per second:
Conversely, if a Boolean ring A is given, we can turn it into a Boolean algebra by defining x ∨ y := x + y + ( x · y ) and x ∧ y := x · y.
Conversely, there are other stars that never rise above the horizon, as seen from any given point on the Earth's surface ( except exactly on the equator ).
Conversely, given a groupoid G in the algebraic sense, let G < sub > 0 </ sub > be the set of all elements of the form x * x < sup >− 1 </ sup > with x varying through G and define G ( x * x < sup >-1 </ sup >, y * y < sup >-1 </ sup >) as the set of all elements f such that y * y < sup >-1 </ sup > * f * x * x < sup >-1 </ sup > exists.
Conversely, given central idempotents a < sub > 1 </ sub >,..., a < sub > n </ sub > in R that are pairwise orthogonal and have sum 1, then R is the direct sum of the rings Ra < sub > 1 </ sub >,…, Ra < sub > n </ sub >.
Given a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.
Conversely, only the wiki users interested in a given project need look at its associated wiki pages, in contrast to high-traffic mailing lists which may burden subscribers with many messages, regardless of their relevance.
Conversely, given a harmonic function, it is the real part of an analytic function, ( at least locally ).
Each convex set containing X must ( by the assumption that it is convex ) contain all convex combinations of points in X, so the set of all convex combinations is contained in the intersection of all convex sets containing X. Conversely, the set of all convex combinations is itself a convex set containing X, so it also contains the intersection of all convex sets containing X, and therefore the sets given by these two definitions must be equal.
Conversely, surveys conducted among living donors postoperatively and in a period of five years following the procedure have shown extreme regret in a majority of the donors, who said that given the chance to repeat the procedure, they would not.
Conversely, given an ordered tree, and conventionally draw the root at the top, then the child nodes in an ordered tree can be drawn left-to-right, yielding an essentially unique planar embedding ( up to embedded homotopy, i. e., moving the edges and nodes without crossing ).
Conversely, the influence of the data at any given point on the initial line propagates with the finite velocity c: there is no effect outside a triangle through that point whose sides are characteristic curves.
Conversely, given any harmonic function in two dimensions, it is the real part of an analytic function, at least locally.
Conversely, if ( A, m, e, inv ) is a group object in one of those categories, then m necessarily coincides with the given operation on A, e is the inclusion of the given identity element on A, inv is the inversion operation and A with the given operation is an abelian group.
Conversely, if the Turing Machine is expected polynomial-time ( for any given x ), then a considerable fraction of the runs must be polynomial-time bounded, and the coin sequence used in such a run will be a witness.
Conversely, suppose we are given ( U, V, W ) satisfying
Conversely, given any ring, we can form a category by taking objects A < sub > n </ sub > indexed by the set of natural numbers ( including zero ) and letting the hom-set of morphisms from to be the set of-by-matrices over, and where composition is given by matrix multiplication.
Conversely, it is hard to believe, given the length and intensity of the struggle between Máel Sechnaill and Brian, that the High King would surrender his title without a fight.
Conversely, an algorithm to test for solvability in arbitrary integers could be used to test a given equation for solvability in natural numbers by applying that supposed algorithm to the equation obtained from the given equation by replacing each unknown by the sum of the squares of four new unknowns.
Conversely, a disease that is easily transmitted but has a short duration might spread widely during 2002 but is likely to have a low prevalence at any given point in 2003 ( due to its short duration ) but a high incidence during 2002 ( as many people develop the disease ).
Conversely, given a commutative diagram, it defines a poset category:

Conversely and algebra
Conversely, any algebra whose associator is alternating is clearly alternative.
Conversely, any algebra for which this is true is clearly alternative.
Conversely, many theorems that hold in universal algebra do not generalise all the way to category theory.
Conversely, once a basis for A has been chosen, the products of basis elements can be set arbitrarily, and then extended in a unique way to a bilinear operator on A, i. e., so the resulting multiplication satisfies the algebra laws.
Conversely, for any topology the clopen ( i. e. closed and open ) subsets yield a Boolean algebra.
Conversely, given any topological space X, the collection of subsets of X that are clopen ( both closed and open ) is a Boolean algebra.
Conversely, symmetric tensors are defined as invariants: given the natural action of the symmetric group on the tensor algebra, the symmetric tensors are the subspace on which the symmetric group acts trivially.
Conversely, the normed division algebras immediately give rise to trialities by taking each V < sub > i </ sub > equal to the division algebra, and using the inner product on the algebra to dualize the multiplication into a trilinear form.
Conversely, given a generalized Cartan matrix, one can recover its corresponding Lie algebra.
Conversely, given any Lie algebra with a direct sum decomposition satisfying these three conditions, the linear map σ, equal to the identity on and minus the identity on, is an involutive automorphism.

Conversely and whose
Conversely, the existence of Bletchley Park, and of the decrypting achievements there, was never officially shared with the Soviet Union, whose war effort would have greatly benefited from regular decrypting of German messages relating to the Eastern Front.
Conversely, since Imhotep was known as the " Son of Ptah ," his mother was sometimes claimed to be Sekhmet, the patron of Upper Egypt whose consort was Ptah.
Conversely, there have been a number of popes whose reign lasted less than a month.
Conversely, citizens may find themselves ineligible because they do not currently reside within the United States ; exceptions apply for children of military parent ( s ) who were born overseas, were disabled or became blind overseas, or first applied for benefits overseas and for students studying abroad who were eligible for SSI in the month prior to leaving the US, whose absence will be for less than 1 year, and who are studying to enhance their ability to perform substantial gainful activity, sponsored by an educational institution in the US, and would not be available to the individual in the US.
Conversely, nominating the party leader whose party maintains a plurality and who are already familiar with their party manifesto facilitates a smoother nomination process.
Equipped with this notion of length, a Riemannian manifold is a metric space, meaning that it has a distance function d ( p, q ) whose value at a pair of points p and q is the distance from p to q. Conversely, the metric tensor itself is the derivative of the distance function ( taken in a suitable manner ).
Conversely, nominating the party leader whose party maintains a plurality and who are already familiar with their party manifesto facilitates a smoother nomination process.
* Conversely, a wave whose phase drifts quickly will have a short coherence time.
Conversely, the valuation on a discrete valuation ring can be extended to a valuation on the quotient field giving a discrete valued field, whose associated discrete valuation ring is just.
Conversely this book, whose discovery is touted in 2 Kings, was therefore believed to have been of an early enough authorship to validate, not only its inclusion, but the book's ultimate placement as the 5th of the " Five Books of Moses ".
Conversely, Clover points out that the villain of slasher films is often a male whose masculinity, and sexuality more generally, are in crisis.
To a graph G there corresponds a signed complete graph Σ on the same vertex set, whose edges are signed negative if in G and positive if not in G. Conversely, G is the subgraph of Σ that consists of all vertices and all negative edges.
Conversely, in the United States Navy, the term " shipmate " can be the derogatory term used by officers and senior enlisted to refer to a sailor whose name they have not bothered to remember or read off of their uniform ( Example: Hey!

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