Conversely, let G be any polynomial such that Af.

Conversely, any algebra whose associator is alternating is clearly alternative.

Conversely, any algebra for which this is true is clearly alternative.

Conversely, a subset R defines a binary function if and only if, for any x in X and y in Y, there exists a unique z in Z such that ( x, y, z ) belongs to R.

Conversely the equilibrium position is said to be " far to the left " if hardly any product is formed from the reactants.

* The spectrum of any bounded linear operator on a Banach space is a nonempty compact subset of the complex numbers C. Conversely, any compact subset of C arises in this manner, as the spectrum of some bounded linear operator.

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, corresponding to any partition of X, there exists an equivalence relation ~ on X.

Conversely, any surjection between sets determines a partition on its domain, the set of preimages of singletons in the codomain.

Conversely, Derek Bickerton and others argue that the advent of abstract words provided a mental basis for analyzing higher-order relations, and that any communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language.

Conversely any planar graph can be formed from a map in this way.

Conversely, a person may feel like he belongs to one state without having any legal relationship to it.

Conversely, the interior of the box has a constant, zero potential energy .< ref > Actually, any constant, finite potential can be specified within the box.

Conversely, extremely thin jewelry can cause the same tearing in what is commonly referred to as the " cheese cutter effect ", either during sudden torsion or over a long period of wearing, especially if the thin jewelry bears any weight.

Conversely, any Hermitian positive semidefinite matrix M can be written as M = A < sup >*</ sup > A ; this is the Cholesky decomposition.

Conversely, if a double sharp were added to any other note not containing a sharp or flat as indicated by the key signature then the note will be raised two semitones or a whole step with respect to the chromatic scale.

Conversely in rings with unity, any simple left R module arises this way.

Conversely, supplementation with L-phenylalanine, L-tyrosine, L-DOPA, or any of the cofactors will increase their respective concentrations.

Conversely, any choice of μ, full rank matrix U, and positive diagonal entries Λ < sub > i </ sub > yields a non-singular multivariate normal distribution.

Conversely, in the absence of spatial continuity can take any value.

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 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.

It is a fact that the ring is a principal ideal ring ; that is, for any ideal I in, there exists an integer n in I such that every element of I is a multiple of n. Conversely, the set of all multiples of an arbitrary integer n is necessarily an ideal, and is usually denoted by ( n ).

) Conversely, it is often helpful to use the geometry of Cartesian coordinates in two or three dimensions to visualize algebraic relationships between two or three of many non-spatial variables.

If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.

Conversely, if either of these last two expressions is defined, then so is the other ( and again they are equal ).

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, the two sunniest months of the year ; both in winter-June and July, both receive an abundant daily average of 9. 0 hours of sunshine.

Conversely, if God is incapable of being incapable, then the two inabilities cancel each other out, making God have the capability to do something.

Conversely, in 2004 the South Korean government charged the Korean High Speed Rail Construction Authority, a public entity, to construct its high speed rail line, 412 km from Seoul to Busan, in two phases.

Conversely, two of the most famous rock musicians from Ontario, Avril Lavigne and Alanis Morissette, are Franco-Ontarian by the second definition but not by the first, since they were born to Franco-Ontarian parents but currently work and live predominantly using the English language ( both currently have residences in Los Angeles ).

Conversely, Francesca Folan played two very different characters: Madeline Bassett in series one and Lady Florence Craye in series four.

Conversely, some view that Sunni jurisprudence falls into two groups: Ahl al-Ra ' i, or people of opinions, due to their emphasis on scholarly judgment and reason ; and Ahl al-Hadith, or people of traditions, due to their emphasis on restricting juristic thought to only what is found in scripture.

Conversely the index theorem for an elliptic complex can easily be reduced to the case of an elliptic operator: the two vector bundles are given by the sums of the even or odd terms of the complex, and the elliptic operator is the sum of the operators of the elliptic complex and their adjoints, restricted to the sum of the even bundles.

Conversely, Y-adapter cables are available that allow two separate joysticks to be connected to a single DA15 game adapter port ; if a joystick connected to one of these Y-adapters has more than two axes or buttons, only the first two of each will work.

Conversely, a connection on E determines a connection on F ( E ), and these two constructions are mutually inverse.

Conversely, in multiprocessor ( or multicore ) systems, there are two or more processing elements working at the same time, and so it is possible that they simultaneously access the same memory location.

Conversely, less than one Yellow Warbler nest in three on average suffers from predation in one way or another, while two out of three Mangrove and Golden Warbler nests are affected.

Conversely, where extra strength but the smooth drive of a smaller pitch is required, the chain may be " siamesed "; instead of just two rows of plates on the outer sides of the chain, there may be three (" duplex "), four (" triplex "), or more rows of plates running parallel, with bushings and rollers between each adjacent pair, and the same number of rows of teeth running in parallel on the sprockets to match.

Conversely, two unitary district councils added the word " county " to their titles to become " Rutland County Council District Council " and " County of Herefordshire District Council ".

Conversely, vocational schools are Government-owned or at least Government-supported institutions, occupy two full years of study, their credits are by and large accepted elsewhere in the academic world and in some instances such as charter academies or magnet schools may take the place of the final years of high school.

Conversely if f is a homomorphism from G to K < sub > k </ sub >, then one can color G by using the same color for two vertices in G whenever they are both mapped to the same vertex in K < sub > k </ sub >.