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These proofs can be carried over to infinite groups by replacement of the average with an integral, provided that an acceptable notion of integral can be defined.
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These and proofs
These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.
These are called conditional proofs: the conjectures assumed appear in the hypotheses of the theorem, for the time being.
These " proofs ", however, would fall apart if it turned out that the hypothesis was false, so there is considerable interest in verifying the truth or falsity of conjectures of this type.
These principles are widely used intuitively in various kinds of proofs, demonstrations and investigations, in addition to being fundamental to experimental design.
These proofs require some background in modular arithmetic.
These proofs are based on the validity of Lorentz invariance and the Principle of locality in the interaction of quantum fields.
" These are the Ayat ( proofs, evidences, verses, lessons, revelations, etc.
These were proffered as " proofs " authenticating the factual basis of his story.
These living and visible proofs of the existence of the concealed Imams are known in Ismaili doctrine as hujjat ( proof ).
These similarities allow one to construct umbral proofs, which, on the surface cannot be correct, but seem to work anyway.
* and These give the proofs and some applications of the results announced in the previous paper.
These are uncirculated coins that have been specially packaged, and ( unless a scarce coin is included ) are generally neither as expensive nor as valuable as proofs.
These proofs were modeled upon Ken Ribet's proof of the converse to Herbrand's theorem ( so-called Herbrand-Ribet theorem ).
These leaves were optional unless traveling to the other former Soviet republics which continued to accept Soviet passports ; for other occasions, other proofs of citizenship were accepted as well.
These chapters can be thought of as a summary of existing knowledge, although Dirichlet simplifies Gauss ' presentation, and introduces his own proofs in some places.
* These proofs are cited in the name of Haym Soloveitchik in Dan ’ s article.
These proofs can be carried over to locally compact groups by replacement of the average with the Haar integral.
These were issued as prints in the early 1520s, sometimes wrongly called " proofs ", and when they were published in book form in 1538, with added verses, the prefactory matter only referred to Lützelburger, it having apparently been forgotten that Holbein was involved.
These proofs are used in the article Addition of natural numbers.
These NASA emblems should be reproduced only from original reproduction proofs, transparencies, or computer files available from NASA Headquarters.
These proofs use the Axiom of choice ( so called non-effective proof ).
These he arranged and stated clearly in the form of aphorisms, with logical deductions, establishing them by proofs drawn from the archives of the council of state.
These and can
These seem about the only two ways in which the `` unhappy incident '' can now be closed.
These engines can be removed from a boat with relative ease, wherein lies their greatest advantage.
These can also move a short distance but at right angles to the tappets.
These are beginnings, but correctly learned they prepare for satisfying and exciting stunts that can be performed by a strong, flexible body ( we are not talking of eccentric extremes ).
These frequencies are amplified and detected by the FM receiver after each burst of transmitted energy and, after the `` pill '' has been calibrated, precise internal pressure indications can be obtained.
These factors can make the difference between waste and efficiency in any benefit program.
These experiments can be considered exploratory only.
These societies can expect to face difficult times.
These records, when systematically maintained, provide much information about the children, which the teacher can use in guidance, instruction, grouping, and reporting to parents.
These can be referred to as operational intelligence and environmental intelligence.
These theoretical relationships are more clearly illustrated in Fig. 7 and their sum can be seen to correlate in form with practical measurements made with the Hesiometer as illustrated in the first portion of Fig. 5 for the cutting mechanism.
These dynamic relationships, between what can be observed on the ground, as opposed to what can be observed by compiling many local observations remain fundamental in any kind of anthropology, whether cultural, biological, linguistic or archaeological.
These are not used in amoeboid movement, but are stiff skeletons on which organelles are supported or can move on.
These can range from simple spelling changes and word forms to switching the entire writing system itself, as when Turkey switched from the Arabic alphabet to a Turkish alphabet of Latin origin.
These finishes protect the adobe wall from water damage, but need to be reapplied periodically, or the walls can be finished with other nontraditional plasters providing longer protection.
These deficits can vary depending on which cerebellar structures have been damaged, and whether the lesion is bilateral or unilateral.
These include all quadratic surds, all rational numbers, and all numbers that can be formed from these using the basic arithmetic operations and the extraction of square roots.
These frequencies can be used to study geological phenomena such as earthquakes.
These are naturally in a ground state but can be excited
These constructions can convey shape, size, motion, location, movement, stative-descriptive, and / or handling information.
These particles continue to decay, emitting alpha particles which can damage cells in the lung tissue.
These conditions can be used to handle unusual situations.
These antigens can sometimes be presented by tumor cells and never by the normal ones.
These can be as simple as a searchlight for a police helicopter or as complicated as the tactical system for an airborne early warning platform.
1.958 seconds.