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 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 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.

Conversely, in functional code, the output value of a function depends only on the arguments that are input to the function, so calling a function f twice with the same value for an argument x will produce the same result f ( x ) both times.

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, 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 we have a b if and only if a < b or a ~ b. This is the reason for using the notation ""; "≤" can be confusing for a preorder that is not anti-symmetric, it may suggest that a ≤ b implies that a < b or a

Conversely, Baptists are underrepresented, a reflection of their quite recent expansion in numbers ; there has been only one Roman Catholic president, although they are currently the largest single denomination, and there have been no Lutheran, Pentecostal, or Latter Day Saint presidents.

Conversely, birds of prey-which show distinct reverse sexual dimorphism — tend to be monogamous for long periods or mate for life ; some species like the Snail kite will choose new mates every year, polygyny is noted in many Harriers and polyandry has been observed in the Harris ' Hawk ( notable for being the only bird of prey to regularly live and hunt in family and social groups ) and the aforementioned Galapagos hawk.

Conversely, a metrizable space is separable if and only if it is second countable, which is the case if and only if it is Lindelöf.

Conversely, jumper classes are scored objectively, based entirely on a numerical score determined only by whether the horse attempts the obstacle, clears it, and finishes the course in the allotted time.

Conversely, if children are found to only develope after undergoing treatment it would challenge the traumagenic model.

Conversely, of the 253 known stable nuclides, only five have both an odd number of protons and odd number of neutrons: hydrogen-2 ( deuterium ), lithium-6, boron-10, nitrogen-14, and tantalum-180m.

Conversely, a German controlled major rail head lay only to the north of their positions.

Conversely, a wing dam is a structure that only partly restricts a waterway, creating a faster channel that resists the accumulation of sediment.

Conversely, a small farm surrounding the owner's dwelling is called a smallholding and is generally focused on self-sufficiency with only the surplus being sold.

Conversely, abstract patterns in science, maths, or language may be observable only by analysis.

Conversely, Hill would play only 47 games in the following four seasons due to a recurring ankle injury.

Conversely, even though nearly 60 percent of voters selected the Democratic Governor Gary Locke in 2000, in 2004 the Democratic gubernatorial nominee Christine Gregoire received only 41 percent of the vote.

Conversely, North Korea refused to speak in the context of six-party talks, stating that it would only accept bilateral talks with the United States.

Conversely, following the diurnal motion with the camera, to eliminate it on the photograph, can best be done with an equatorial mount, which requires adjusting the right ascension only ; a telescope may have a motor to do that automatically ( sidereal drive ).

Conversely, if a source file's modification time is in the future, it triggers unnecessary rebuilding, which may inconvenience users.

Conversely, the ease and simplicity of dBase presented a challenge as its users became more expert and as professional programmers were drawn to it.

Conversely, users can view content only at or below their own security level ( i. e. secret researchers can view public or secret files, but may not view top-secret files ; no read-up ).

Conversely, the users of some innovative pronunciations such as " Febuary " ( for February ) may regard the historically ( and phonetically ) authentic version as a pedantic spelling pronunciation.

Conversely, users can only view content at or above their own integrity level ( a monk may read a book written by the high priest, but may not read a pamphlet written by a lowly commoner ).

Conversely, overly long retention can overwhelm users with slow computers or network connections by making the article lists inordinately large.

" Conversely, he says of hashish users: " Ho there!

Conversely, they are interested in the role of vegetation on climate and weather.

Conversely, someone's " dance card is full " implies that even though they may be interested, they have no time for another person.

Conversely, some applications of geophones are interested only in very local events.

Conversely, Gaddafi was more interested in a complete merging of Libya and Tunisia into the Arab Islamic Republic.

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, 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: