However, if the approximation is defined asymptotically, for example by saying that two functions f and g are approximately equal near some point if the limit of f-g is 0 at that point, then this defines an equivalence relation.

However, the approach of Neyman does not rely on a repeated-sampling scenario, so that there is no direct equivalence.

However, at the current level of accuracy, these observations cannot distinguish between general relativity and other theories in which the equivalence principle is valid.

However these negotiations may prove difficult in that both parties in a conflict believe that they are morally superior to the other, and are unwilling to negotiate on basis of moral equivalence.

However a phoneme is generally regarded as an abstraction of a set ( or equivalence class ) of speech sounds ( phones ) which are perceived as equivalent to each other in a given language.

) However, this was understood ( only ) in the language of equivalence classes of quadratic forms, so that in particular the analogy between quadratic forms and the Fermat equation seems not to have been perceived.

However, these symbols are also used for material equivalence ; the proper interpretation depends on the context.

However, Ricardo himself was skeptical of this equivalence.

However, the DIAMOND has shown rough equivalence of efficacy between a " step-up " approach to therapy ( antacids, followed by histamine antagonists, followed by PPIs ) and a " step-down " approach ( the reverse ).

However, there is a formula for finding the number of relations that are simultaneously reflexive, symmetric, and transitive – in other words, equivalence relations –, those that are symmetric and transitive, those that are symmetric, transitive, and antisymmetric, and those that are total, transitive, and antisymmetric.

However, any difference between inertial and gravitational mass would violate the equivalence principle of general relativity.

However, Polish spaces are primarily studied today because they are the primary setting for descriptive set theory, including the study of Borel equivalence relations.

However, this equivalence between L < sub > 1 </ sub > and L < sub >∞</ sub > metrics does not generalize to higher dimensions.

However, Einstein was the first scientist to propose the E = mc < sup > 2 </ sup > formula and the first to interpret mass – energy equivalence as a fundamental principle that follows from the relativistic symmetries of space and time.

However, two basic principles must be adhered to: " equivalence " ( the procedure for EU cases must be equivalent to the procedure for domestic cases ) and " effectiveness " ( the procedure cannot render the law functionally ineffective ).

However, an actual overpayment will generally occur only if the winner fails to account for the winner's curse when bidding ( an outcome that, according to the revenue equivalence theorem, need never occur ).

However, the objective should be to provide equivalence with the security and privacy of

However, in absorbing photons, the dust acquires added mass via mass-energy equivalence.

However, if sets whose symmetric difference has measure zero are identified into a single equivalence class, the resulting quotient set can be properly metrized by the induced metric.

Thus Q defines an inner product on dom T. Let H < sub > 1 </ sub > be the completion of dom T with respect to Q. H < sub > 1 </ sub > is an abstractly defined space ; for instance its elements can be represented as equivalence classes of Cauchy sequences of elements of dom T. It is not obvious that all elements in H < sub > 1 </ sub > can identified with elements of H. However, the following can be proved:

However, AMD used what it called a PR rating, or performance rating, to label the chips according to their equivalence to a Pentium of that clock speed.

However, this acceleration does not show up in the orbits of the outer planets, so any generic gravitational answer would need to violate the equivalence principle ( see modified inertia below ).

However some Universities continue to hand out so-called equivalence certificates that certify the equivalence of a Dipl .- Ing.

However, some have argued that equivalence is not clearly stated in DSM-IV-TR.

However, he does not immediately show what this principle might be.

However, he did believe that a non-scientific " guiding principle " governed the universe and human life.

" However French government applies a principle of precaution against GMO.

However, in many jurisdictions the members of the company are permitted to ratify transactions which would otherwise fall foul of this principle.

However, since Cardinal Quignonez's attempt to reform the Breviary employed this principle — albeit with no regard to the traditional scheme — such notions had floated around in the western Church, and can particularly be seen in the Paris Breviary.

However, stare decisis, the principle that similar cases should be decided according to consistent principled rules so that they will reach similar results, lies at the heart of all common law systems.

However, many of them oppose abortion, as they see it as a positive liberty and violates the non-aggression principle because abortion is aggression towards the fetus.

However, the principle of operation might be more precisely described as gas-jet pump, since diffusion plays a role also in other high vacuum pumps.

However, in principle, since the same electronegativities should be obtained for any two bonding compounds, the data is in fact overdetermined, and the signs are unique once a reference point is fixed ( usually, for H or F ).

However, the principle of locality appeals powerfully to physical intuition, and Einstein, Podolsky and Rosen were unwilling to abandon it.

However, quantum field theories that are " local " in this sense appear to violate the principle of locality as defined by EPR, but they nevertheless do not violate locality in a more general sense.

However, this article provides an interesting discussion of the limitations of the principle and also of different scientists ' views as to whether it is an accurate representation of reality or whether " Huygens ' principle actually does give the right answer but for the wrong reasons ".

However, the principle of special relativity generalizes the notion of inertial frame to include all physical laws, not simply Newton's first law.

However, either fission or fusion technologies can in principle achieve velocities far higher than needed for Solar System exploration, and fusion energy still awaits practical demonstration on Earth.

However, she argues this a distortion of " a healthy relationship of mutual submission " actually specified in Christian doctrine where " ove is based on a deep, mutual respect as the guiding principle behind all decisions, actions, and plans ".

However, such kernel features are incompatible with the minimality principle, and are thus not provided in modern microkernels, which instead rely on appropriate user-level protocols.

However, a more detailed analysis based on the Archimedean principle and the densities of magnesium and its combustion product shows that just being lighter than air cannot account for the increase in mass.

However, common law jurisdictions usually do not have the principle of good faith in commercial contracts, therefore it is inappropriate to state that pacta sunt servanda includes the principle of good faith.

However, stability of large systems with many electrons and many nuclei is a different matter, and requires the Pauli exclusion principle.

However, this theory needs to be generalized in ( 2 + 1 ) or ( 3 + 1 ) dimensions although, in principle, the field equations are amenable to such generalization as shown with the inclusion of a one-graviton process and yielding the correct Newtonian limit in d dimensions if a dilaton is included.

However, recent developments attempt to show that if locality is only approximate and the holographic principle is correct, the Weinberg – Witten theorem would not be valid.

However, the Prussian and other German armies were delayed for months at the Siege of Metz and the Siege of Paris, due to the greatly increased firepower of the defending infantry, and the principle of detached or semi-detached forts with heavy-caliber artillery.