Page "Kernel (set theory)" ¶ 19
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## Some Related Sentences

Conversely and if
Conversely, if statistics were uncovered which contradicted a cherished theory, the sources were denounced as faulty.
Conversely, experimenters would consider as impressive such statements as the following, which, if they turned out to be hits, are so unusual as to be really significant:
Conversely, if he gives a heavy rating to his own reading, and finds more accurate facts in it than in the others, a point is chalked up for the intrinsic, objective meaningfulness of this type of mediumistic material.
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, 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 if you do have a better product suddenly you have these businesses that grow like topsy.
Conversely, if the second theory is correct, then the Athenians were merely reacting to the Persians attacking them.
Conversely the equilibrium position is said to be " far to the left " if hardly any product is formed from the reactants.
Conversely, negative chemotaxis occurs if the movement is in the opposite direction.
Conversely, if ƒ: C → C is a function which is differentiable when regarded as a function on R < sup > 2 </ sup >, then ƒ is complex differentiable if and only if the Cauchy – Riemann equations hold.
Conversely, if the same is done with the left hand, a left-handed system results.
Conversely, if the amount of fat is increased, increasing the number of calories ingested will only add weight.
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.
Conversely every partition of comes from an equivalence relation in this way, according to which if and only if and belong to the same set of the partition.
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 the measured potential is negative, the electrode is more oxidizing than the SHE ( such as Zn in ZnSO < sub > 4 </ sub > where the standard electrode potential is − 0. 76 V ).
Conversely, if the firm is able to get bulk discounts of an input, then it could have economies of scale in some range of output levels even if it has decreasing returns in production in that output range.
Conversely, if no advantage is gained from kicking the ball, play should continue.
Conversely, daylight stock shot in daylight will look normal, but orange if shot under tungsten lights.
Conversely, if the data are sparse — that is, if only K out of N Fourier coefficients are nonzero — then the complexity can be reduced to O ( K log N log ( N / K )), and this has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm ( which estimates the largest K coefficients to several decimal places ).

Conversely and X
Conversely, British English favours fitted as the past tense of fit generally, whereas the preference of American English is more complex: AmEng prefers fitted for the metaphorical sense of having made an object " fit " ( i. e., suited ) for a purpose ; in spatial transitive contexts, AmEng uses fitted for the sense of having made an object conform to an unchanged object that it surrounds ( e. g., " fitted X around Y ") but fit for the sense of having made an object conform to an unchanged object that surrounds it ( e. g., " fit X into Y "); and for the spatial senses ( both intransitive and transitive ) of having been matching with respect to contour, with no alteration of either object implied, AmEng prefers fit (" The clothes fit.
* Conversely, corresponding to any partition of X, there exists an equivalence relation ~ on X.
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.
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.
We define Thm ( C ) to be the set of all formulas that are valid in C. Conversely, if X is a set of formulas, let Mod ( X ) be the class of all frames which validate every formula from X.
) Conversely, if B satisfies both of the conditions 1 and 2, then there is a unique topology on X for which B is a base ; it is called the topology generated by B.
Conversely, if R is a symmetric relation over a set X, one can interpret it as describing an undirected graph with the elements of X as the vertices and the pairs in R as the edges.
A hypergraph H may be represented by a bipartite graph BG as follows: the sets X and E are the partitions of BG, and ( x < sub > 1 </ sub >, e < sub > 1 </ sub >) are connected with an edge if and only if vertex x < sub > 1 </ sub > is contained in edge e < sub > 1 </ sub > in H. Conversely, any bipartite graph with fixed parts and no unconnected nodes in the second part represents some hypergraph in the manner described above.
for some real-valued functions a and b depending, respectively, on x and y. Conversely, given any such pair of real-valued functions, there exists a vector field X satisfying 1. and 2.
Conversely, if X is projective, then the pullback of under the closed immersion of X into a projective space is very ample.
Conversely, a complete variety is close to being a projective variety: Chow's lemma states that if X is a complete variety, there is a projective variety Z and a birational morphism Z → X.

Conversely and is
Conversely, suppose that **ya is in the null space of Af.
Conversely, a current of one ampere is one coulomb of charge going past a given point per second:
Conversely, an adiabatic process that is irreversible and extracts no work is in an isenthalpic process, such as viscous drag, progressing towards a nonnegative change in entropy.
Conversely, any algebra whose associator is alternating is clearly alternative.
Conversely, any algebra for which this is true is clearly alternative.
Conversely the use of true brass seems to have declined in Western Europe during this period in favour of gunmetals and other mixed alloys but by the end of the first Millennium AD brass artefacts are found in Scandinavian graves in Scotland, brass was being used in the manufacture of coins in Northumbria and there is archaeological and historical evidence for the production of brass in Germany and The Low Countries areas rich in calamine ore which would remain important centres of brass making throughout the medieval period, especially Dinant – brass objects are still collectively known as dinanterie in French.
Conversely, because space is expanding, and more distant objects are receding ever more quickly, light emitted by us today may never " catch up " to very distant objects.
Conversely, modern biological sciences ( including even concepts such as molecular ecology ) are intimately entwined and dependent on the methods developed through biotechnology and what is commonly thought of as the life sciences industry.
Conversely it may generate too many points in areas where the curve is close to linear.
Conversely, every Bayesian procedure is admissible.
Conversely, the islands do not receive the upwellings ( cold streams ) that affect the West African coast, so the air temperature is cooler than in Senegal, but the sea is actually warmer, because the orographic relief of some islands, as Sao Miguel with steep mountains, cover it with rich woods and luxuriant vegetation where the dense moisture condense and soak the plants, rocks, soil, logs, moss etc.
Conversely in francophone Canada, one hundredth of a Canadian dollar is informally called a sou ( penny ), though cent is official in both English and French.
Conversely, an absence of secure cycle-parking is a recurring complaint by cyclists from cities with low modal share of cycling.
* 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.

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