Page "Equivalence relation" ¶ 57
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## Some Related Sentences

Conversely and any
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, 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 and between
Conversely, in more recent times, Russian existentialist philosopher Lev Shestov viewed Job as the embodiment of the battle between reason ( which offers general and seemingly comforting explanations for complex events ) and faith in a personal god, and one man's desperate cry for him.
) 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.
Conversely, if the source of waves is moving away from the observer, each wave is emitted from a position farther from the observer than the previous wave, so the arrival time between successive waves is increased, reducing the frequency.
That is, the motivational internalist believes that there is an internal, necessary connection between one's conviction that X ought to be done and one's motivation to do X. Conversely, the motivational externalist ( or moral externalist ) claims that there is no necessary, internal connection between moral convictions and moral motives.
Conversely, from a partial order on a partition of a set S one can construct a preorder on S. There is a 1-to-1 correspondence between preorders and pairs ( partition, partial order ).
Conversely, Per Christiansen found that using skull morphology allowed him to identify the subspecies krugeri, nubica, persica, and senegalensis, while there was overlap between bleyenberghi with senegalensis and krugeri.
Conversely, mapping the data flow between the components determines the logical topology of the network.
Conversely, a particular map between particular objects may be called an unnatural isomorphism ( or " this isomorphism is not natural ") if the map cannot be extended to a natural transformation on the entire category.
Conversely the Jupiter-family comets are believed to originate in the Kuiper belt, a flat disc of icy debris between 30 AU ( Neptune's orbit ) and 50 AU from the Sun ( in the scattered disc ).
Conversely, reviewers sharply criticized " long and frequent loading " between areas and battles due to poor emulation.
As stated earlier, an adjunction between categories C and D gives rise to a family of universal morphisms, one for each object in C and one for each object in D. Conversely, if there exists a universal morphism to a functor G: C → D from every object of D, then G has a left adjoint.
Conversely, if a ship is to safely pass under a low bridge or overhead power cable, the mariner must know the minimum clearance between the masthead and the obstruction, which will occur at high tide.
Conversely, the north ( on the " rive droite ") has a gentle depression to about above sea level ( at Saint-Marceau ) between the Loire and the Loiret, designated a " zone inondable " ( flood-risk zone ).
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, British Decca retained a non-reciprocal right to license and issue American Decca recordings in the UK on their Brunswick Records ( US Decca recordings ) and Coral Records ( US Brunswick and Coral recordings ) labels ; this arrangement continued through 1967 when a UK branch of MCA was established utilising the MCA Records label, with distribution fluctuating between British Decca and other English companies over time.
Conversely, there seems to be a negative correlation between maximum sunspot activity and Es activity in Australasia.
Conversely, there seems to be a negative correlation between maximum sunspot activity and Es activity in Australasia.
Conversely, the lower the frequency of recombination between the markers, the smaller the physical distance between them.
Conversely, it took more than 41 seasons after Neun's play before Ron Hansen's performed the feat on July 30, 1968, marking the longest span between unassisted triple plays.
Conversely, the most recent addition of What Witches Do ( 2010 ) includes previously published interviews between Sanders and Farrar.
Conversely, a voltage follower inserted between a small load resistance and a driving stage presents a large load to the driving stage, an advantage in coupling a voltage signal to a small load.
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.

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