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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 principles are widely used intuitively in various kinds of proofs, demonstrations and investigations, in addition to being fundamental to experimental design.
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.
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 ",
Each principle preceded by " Ani Ma ' amin B ' emunah Shleymah ", " I believe with perfect faith that ..." These principles are reflected in the hymn Yigdal.
These include " The Outcasts of Heaven Belt ", " Legacy ", and an upcoming novel featuring Pham Nuwen.
These are of the type known as " inginocchiata ", " kneeling " on two brackets.
The only difference is that in the chorus, instead of singing " These are men, America's best ", they sing " These are men, The Netherlands ' best ".
These could be the classical virtues — courage, temperance, justice, and wisdom — that promoted the Greek ideal of man as the " rational animal ", or the theological virtues — faith, hope, and love — that distinguished the Christian ideal of man as a being created in the image of God.
These layers do not show the tilting and distortion associated with mountain building, therefore, the likeliest explanation is a " regression ", that is, a drop in sea level.
These districts include the Mexican villages, such as Pilsen along 18th street, and La Villita along 26th Street ; the Puerto Rican enclave Paseo Boricua in the Humboldt Park neighborhood ; " Greektown ", along South Halsted St, immediately west of downtown ; " Little Italy ", along Taylor St ; " Chinatown "; " Polish Patches "; " Little Seoul ", around Lawrence Avenue ; a cluster of Vietnamese restaurants along Argyle Avenue near Broadway, and Indian / Pakistani along Devon Avenue.
These skillfully rendered paintings encouraged fan Glenn Bray to ask Barks if he could commission a painting of the ducks (" A Tall Ship and a Star to Steer Her By ", taken from the cover of Walt Disney's Comics and Stories # 108 by Barks ).
These included the Sanyo ICC-0081 " Mini Calculator ", the Canon Pocketronic, and the Sharp QT-8B " micro Compet ".
These included: " My Dreams Are Getting Better All The Time ", " Till The End of Time ", " Come To Baby Do ", and " I Got the Sun in the Mornin '".
The Hebrew title is taken from the opening phrase Eleh ha-devarim, " These are the words ..."; the English title is from a Greek mis-translation of the Hebrew phrase mishneh ha-torah ha-zoth, " a copy of this law ", in, as to deuteronomion touto-" this second law ".
These resolutions are formalized by an " Exchange of Notes ", or, since 2001, an " Exchange of Letters ".
These values, used by the pattern's author to determine which solution is " best ", must also be documented within the pattern.
These shows have featured large collections of his gridfonts, his ambigrams ( pieces of calligraphy created with two readings, either of which is usually obtained from the other by rotating or reflecting the ambigram, but sometimes simply by " oscillation ", like the Necker Cube or the rabbit / duck figure of Joseph Jastrow ), and his " Whirly Art " ( music-inspired visual patterns realized using shapes based on various alphabets from India ).
These Daleks presumably become the " Imperial Daleks ", first seen in Remembrance of the Daleks.
These differences stem from the threshold chosen for describing an extinction event as " major ", and the data chosen to measure past diversity.
These cost from 0 to 3 or more points depending on whether they should be considered Frequent, Major ( or even " Twice Major ", for especially powerful abilities that significantly affect gameplay ) and / or Versatile.
These stones were initially sold under the names " Emerita " and " Symeralds ", and they were grown as a thin layer of emerald on top of natural colorless beryl stones.

These and however
These are not, however, differences in federal structure.
These principles, however, will not be served by violence in any form.
These little songs, however, were sweet nothings from the heart, tender memories of his childhood, little melodies that anyone could hum and that would make one want to weep.
These became `` strays '', the term bein' restricted to cattle, however, as hosses, under like circumstances, were spoken of as `` stray hosses '', not merely `` strays ''.
These qualities alone, however, would not account for their success, and it took me a while to discover the crowning virtue that completes this company's collective personality.
These, however, are exceptions.
These applications are declining, however.
These ordinances proved, however, generally ineffectual to secure strictness of diet, and contemporaneous literature abounds with satirical remarks and complaints concerning the inordinate extravagance of the tables of the abbots.
These authors proved, however, that no optical system can justify these suppositions, since they are contradictory to the fundamental laws of reflexion and refraction.
These conclusions were, however, questioned by another review, which found that clozapine, amisulpride, and olanzapine and risperidone were more effective Clozapine has appeared to be more effective than other atypical antipsychotics, although it has previously been banned due to its potentially lethal side effects.
These fish can still, however, find their way around by means of their lateral lines, which are highly sensitive to fluctuating water pressure.
These tests are created ideally through collaboration between business customers, business analysts, testers and developers, however the business customers ( product owners ) are the primary owners of these tests.
These elections constitutionally must be held no longer than every five years apart, however elections can be called whenever the Government so chooses to seek a new mandate or loses a vote of no confidence in Parliament.
( These are actually referred to in the translation as " balls "; however, they were clearly intended to be bubbles, since they pop, and are taken from Bubble Bobble.
These were however used as abbreviations in diagrams or procedures ; there was no concept of atoms combining to form molecules.
These programs, however, were never supported by the landholding families, because they favored the peasants.
These names do not use the name " Confucius " at all, but instead center on the figure or ideal of the Confucian scholar ; however, the suffixes of jiā, jiào, and xué carry different implications as to the nature of Confucianism itself.
These frequencies are at the upper range of human hearing and are inaudible to many people ; however, some people ( especially children ) will perceive a high-pitched tone near an operating television CRT.
These claims, however, were unsubstantiated and neither the Rockies nor Paciolan have sought investigation into the matter.
These machines were, however, very heavy and expensive.
These games, however, do not allow the participants to choose how much they drink, as this is dependent on the act of skill.
These terms, however, do not apply to other beneficiaries of government spending such as tax incentives and military spending.
These however may have been a granuloma, or even a post-traumatic neuroma.
These more recent versions, however, maintain that only the subjective, qualitative aspects of mental states are epiphenomenal.

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