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Conversely, if a set of edges forms a forest, then by repeatedly removing leaves from this forest it can be shown by induction that the corresponding set of columns is independent.
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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 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, 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 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, 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 set
Conversely, any surjection between sets determines a partition on its domain, the set of preimages of singletons in the codomain.
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, the symbol width could be set at 8, even if only values 0 and 1 are used ; these data would only require a 2-color table.
Conversely, one-dimensional orthogonal projectors are extreme points of the set of density operators.
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 ).
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.
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 ).
Given a vector space V over a field K, the span of a set S ( not necessarily finite ) is defined to be the intersection W of all subspaces of V which contain S. W is referred to as the subspace spanned by S, or by the vectors in S. Conversely, S is called a spanning set of W.
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, a phonetic character set is written precisely as it is spoken, but with the disadvantage that slight pronunciation differences introduce ambiguities.
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, 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.
Conversely, it being set apart implies the opposite-that someone took the clothes off in an ordinary manner ; furthermore, the Greek text uses the word, entetuligmenon, " having been folded up ", seeming to imply some intentional action had been taken on the soudarion.
Conversely, if X is a Hausdorff space and ker f is a closed set, then the coimage of f, if given the quotient space topology, must also be a Hausdorff space.
Conversely, techniques have been proposed for generating models of GRNs that best explain a set of time series observations.
Conversely and edges
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 ).
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 and forms
Conversely, in the English language as a whole, singular verb forms can often be used with nouns ending in "- s " that were once considered plural ( for example: " Physics is my favorite academic subject ").
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, nimbostratus is coded as middle because it usually initially forms at mid-altitudes of the troposphere and becomes vertically developed by growing downward into the low altitude range.
Conversely, people not familiar with the various different forms of dance may ask for a evening of square dance meaning simply a barn dance where many different formations of dance are used.
Conversely, there are exceptions to their ' original forms being lost ' as in the series, Tobias was able to acquire his original DNA ; and hence was able to change into his original self.
Conversely, there have also been campaigns against potentially dangerous forms of contraception such as defective IUDs.
* Conversely, some authors might haphazardly switch between the subjunctive and indicative forms of verbs, with no intended difference in meaning.
Conversely, poets such as John Milton alternated between short and long forms for function words, depending on whether they occurred on or off the meter.
Conversely, the animated series adhered to the character's intended transformation method of splitting into two forms, save for an animation error in " Surprise Party ", which saw an unusually small Sky Lynx transform directly from shuttle mode to lynx mode and in " The Quintesson Journal " when Sky Lynx transforms from lynx mode to shuttle mode.
Conversely, she is not as central in most forms of established Christianity as she is in Gnosticism, but to some Christian mystics the Sophia is a very important concept.
is a volume form on M. Conversely, given two volume forms, their ratio is a non-vanishing function ( positive if they define the same orientation, negative if they define opposite orientations ).
Conversely, libertarians and anarcho-capitalists most commonly apply the term " anarchism " to any philosophy that opposes all forms of initiatory coercion ( without specifications regarding economic systems ).