Conversely, every Bayesian procedure is admissible.

Conversely, every point on the line can be interpreted as a number in an ordered continuum which includes the real numbers.

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, every formally real field can be equipped with a compatible total order, that will turn it into an ordered field.

Conversely, every preorder is the reachability relationship of a directed graph ( for instance, the graph that has an edge from x to y for every pair ( x, y ) with x ≤ y ).

Conversely, though every president from Washington to John Quincy Adams can be definitely assigned membership in an Anglican or Unitarian body, the significance of these affiliations is often downplayed as unrepresentative of their true beliefs.

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, if the diagonal quantities are zero in every basis, then the wavefunction component:

Conversely every positive functional φ gives a corresponding inner product < ƒ, g >< sub > φ </ sub > = φ ( g * ƒ ).

Conversely, every positive semi-definite matrix is the covariance matrix of some multivariate distribution.

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 we pick every member of the same population with property and ask " what proportion of these have property?

Conversely, every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.

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.

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 ).

This ring is the endomorphism ring of A. Conversely, every ring ( with identity ) is the endomorphism ring of some object in some preadditive category.

Conversely, in a preadditive category, every binary equaliser can be constructed as a kernel.

Conversely, every Polish space is homeomorphic to a G < sub > δ </ sub >- subset of the Hilbert cube.

Conversely, extra lives are earned by collecting heart points, which are earned by defeating enemies or collecting Hearts, with an extra life earned for every 100 points earned.

Conversely the building can be recovered from the BN pair, so that every BN pair canonically defines a building.

Conversely, the following characterization of derived functors holds: given a family of functors R < sup > i </ sup >: A → B, satisfying the above, i. e. mapping short exact sequences to long exact sequences, such that for every injective object I of A, R < sup > i </ sup >( I )= 0 for every positive i, then these functors are the right derived functors of R < sup > 0 </ sup >.

Conversely, every method for evaluating conditionals can be seen as a way for performing revision.

Conversely, we have every opportunity to prevent our lives from being boring.

Conversely, the tiny meson mass mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.

Conversely, by the inverse function theorem, there can be at most one value for σ that, when applied as an input to, will result in a particular value for C.

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

Conversely, inverse iteration based methods find the lowest eigenvalue, so is chosen well away from and hopefully closer to some other eigenvalue.

Conversely, when carbon's hybridization changes from sp < sup > 2 </ sup > to sp < sup > 3 </ sup >, the out of plane bending force constants at the transition state increase and an inverse SKIE is observed with typical values of 0. 8 to 0. 9.

* Inverses: by definition every isomorphism has an inverse which is also an isomorphism, and since the inverse is also an endomorphism of the same object it is an automorphism.

Specifically, it is a non-trivial ring in which every non-zero element a has a multiplicative inverse, i. e., an element x with.

In abstract algebra, a field is a commutative ring which contains a multiplicative inverse for every nonzero element, equivalently a ring whose nonzero elements form an abelian group under multiplication.

From these two axioms, it follows that for every g in G, the function which maps x in X to g · x is a bijective map from X to X ( its inverse being the function which maps x to g < sup >− 1 </ sup >· x ).

For the inverse to be defined on all of Y, every element of Y must lie in the range of the function ƒ.

It can be shown that in every such ring, multiplication is commutative, and every element is its own additive inverse.

If the ranges of the morphisms of the inverse system of abelian groups ( A < sub > i </ sub >, f < sub > ij </ sub >) are stationary, that is, for every k there exists j ≥ k such that for all i ≥ j: one says that the system satisfies the Mittag-Leffler condition.

If is another measurable space then a function is called measurable if for every Y-measurable set, the inverse image is X-measurable i. e..

It also ( originally ) generalized a group ( a monoid with all inverses ) to a type where every element did not have to have an inverse, thus the name semigroup.

A group is then a monoid in which every element has an inverse element.

There is a bijection between every pair of equivalence classes: the inverse of a representative of the first equivalence class, composed with a representative of the second.

In other words, in a monoid every element has at most one inverse ( as defined in this section ).

f. Thus, every pair of ( mutually ) inverse elements gives rise to two idempotents, and ex

An intuitive description of this is fact is that every pair of mutually inverse elements produces a local left identity, and respectively, a local right identity.

If all elements are regular, then the semigroup ( or monoid ) is called regular, and every element has at least one inverse.

If every element has exactly one inverse as defined in this section, then the semigroup is called an inverse semigroup.

In a *- regular semigroup S one can identify a special subset of idempotents F ( S ) called a P-system ; every element a of the semigroup has exactly one inverse a * such that aa * and a * a are in F ( S ).

It is possible to approximate a triangle wave with additive synthesis by adding odd harmonics of the fundamental, multiplying every ( 4n − 1 ) th harmonic by − 1 ( or changing its phase by π ), and rolling off the harmonics by the inverse square of their relative frequency to the fundamental.

The map m is the group operation, the map e ( whose domain is a singleton ) picks out the identity element of the group, and the map inv assigns to every group element its inverse.

Any group can be seen as a category with a single object in which every morphism is invertible ( for every morphism f there is a morphism g that is both left and right inverse to f under composition ) by viewing the group as acting on itself by left multiplication.

" More precisely, a member of the Jacobson radical must project under the canonical homomorphism to the zero of every " right division ring " ( each non-zero element of which has a right inverse ) internal to the ring in question.