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Many theorems from classical geometry hold true for this spherical geometry as well, but many do not ( see parallel postulate ).
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Many and theorems
Many theorems which are provable using choice are of an elegant general character: every ideal in a ring is contained in a maximal ideal, every vector space has a basis, and every product of compact spaces is compact.
Many mathematical theorems can be reduced to more straightforward computation, including polynomial identities, trigonometric identities and hypergeometric identities.
Many logicians believe that Gödel's incompleteness theorems struck a fatal blow to David Hilbert's second problem, which asked for a finitary consistency proof for mathematics.
Many more authors state theorems for Dedekind domains with the implicit proviso that they may require trivial modifications for the case of fields.
Many theorems, which are modeled after Ramsey's theorem itself, assert that in every partition of a large structured object, one of the classes necessarily contains a large structured subobject, but give no information about which class this is.
Many famous conjectures and theorems in number theory would follow immediately from the abc conjecture.
Many theorems and concepts involving graphs also hold for hypergraphs.
Many such theorems will not do so explicitly, as usually stated in standard mathematical language.
Many of these theorems only apply to corrections calculable in perturbation theory and so instantons, which are not seen in perturbation theory, provide the only corrections to these quantities.
Many forms of these theorems are actually known to be equivalent, so that the assertion that " PIT " holds is usually taken as the assertion that the corresponding statement for Boolean algebras ( BPI ) is valid.
Many other Picard-type theorems can be derived from the Second Fundamental Theorem.
Many important min-max theorems in combinatorics can be expressed in these terms.
Many deep theorems on the structure of finite groups use characters of modular representations.
These properties are essentially weaker versions of strong and supercompact cardinals, consistent with V = L. Many theorems related to these cardinals have generalizations to their unfoldable or strongly unfoldable counterparts.
Many fixed-point theorems yield algorithms for locating the least fixed point.
Many and from
Many small bones protruded crazily from the shreds of flesh.
Many home-bound subway riders utilizing the Flushing-Main Street express are daily confronted with the sight of the local departing from the Woodside station as their express comes to a stop, leaving them stranded and strained.
Many of today's developments in thermoforming stem from original work done with signs and displays ; ;
Many workers believe that the response is proportional to the incident momentum of the particles, a relation deduced from laboratory results linearly extrapolated to meteoritic velocities.
Many people use wicker cradles for old red wine, lifting the bottle carefully from the bin into the cradle and eventually to the table, without disturbing the sediment.
Many years later ( on August 3, 1915 ), Lucy Upton wrote Winslow's daughter soon to be graduated from Smith College: `` While I love botany which, after dabbling in for years, I studied according to the methods of that day exactly forty years ago in a summer school, it must be fascinating to take up zoology in the way you are doing.
Many appeared to regard their sexual behavior as a justifiable means of gaining acceptance from and identification with others ; ;
Many are phototrophic, although some groups contain members that are mixotrophic, deriving energy both from photosynthesis and uptake of organic carbon either by osmotrophy, myzotrophy, or phagotrophy.
Many companies are coming into the country from China and surrounding nations to help improve road surfaces.
Many newer brands are alcohol-free and contain odor-elimination agents such as oxidizers, as well as odor-preventing agents such as zinc ion to keep future bad breath from developing.
Many of the Anti-Taurus peaks apparently are recently extinct volcanoes, to judge from extensive lava flows.
Many modern Pueblo tribes trace their lineage from settlements.
Renaissance architects included Alberti, Brunelleschi and Bramante. Many of these artists came from Florence and it remained an important centre for the Renaissance into the 16th century eventually to be overtaken by Rome and Venice.
Many scholars see the persistence of Germanic Arianism as a strategy that was followed in order to differentiate the Germanic elite from the local inhabitants and their culture and also to maintain the Germanic elite's separate group identity.
Many laboratory methods exist for the organic synthesis of arenes from non-arene precursors.
Many of the Ainu dialects, even from one end of Hokkaido to the other, were not mutually intelligible ; however, the classic Ainu language of the Yukar, or Ainu epic stories, was understood by all.
Many illustrious Athenians, including Cimon, Miltiades, Alcibiades and the historian Thucydides, traced their descent from Ajax.
Many officials, including those from Maryland, Virginia and Louisiana, as well as Chief Justice Chase personally, underscored for the President that the Southern states were economically in a state of chaos and governmental disorganization, and most anxious to reach agreements that would restore them to the Union.
Many stars visible to the naked eye have such a low absolute magnitude that they would appear bright enough to cast shadows if they were only 10 parsecs from the Earth: Rigel (− 7. 0 ), Deneb (− 7. 2 ), Naos (− 6. 0 ), and Betelgeuse (− 5. 6 ).
Many arguments from morality are based on morality normativity, which suggest that objective moral truths exist and require God's existence to give them authority.
Many cultures have built devices that travel through the air, from the earliest projectiles such as stones and spears, the boomerang in Australia, the hot air Kongming lantern, and kites.
Evidence for this is found in the prologue to the Gospel of Luke, wherein the author alludes to his sources by writing, " Many have undertaken to draw up an account of the things that have been fulfilled among us, just as they were handed down to us by those who from the first were eyewitnesses and servants of the word.
Many believe this group of texts comes from the original Book of Acts by looking at the Byzantine text for the whole of the New Testament.
Many cultures have attached importance to astronomical events, and the Indians, Chinese, and Mayans developed elaborate systems for predicting terrestrial events from celestial observations.
Many letters look similar but are distinguished from one another by dots () above or below their central part, called.
Many and classical
Many students of literature know that classical defense.
Many Enlightenment thinkers ( such as Adam Smith and the American Founding Fathers ) subscribed to this view to some extent, and it remains influential among so-called classical liberals and libertarians.
Many philosophies and worldviews have a set of classical elements believed to reflect the simplest essential parts and principles of which anything consists or upon which the constitution and fundamental powers of anything are based.
Many modern scholars of liberalism argue that no particularly meaningful distinction between classical and modern liberalism exists.
Many classical deists were critical of some types of prayer.
Many results in classical thermodynamics are not easily applied to non-equilibrium systems.
Many Asian civilizations distinguish between art / court / classical styles and " folk " music, though cultures that do not depend greatly upon notation and have much anonymous art music must distinguish the two in different ways from those suggested by western scholars.
Many pictures released from the 1960s onward share attributes with film noir of the classical period, and often treat its conventions self-referentially.
Many modern soloists ( following the lead of Paco de Lucía ) play what is called a flamenca negra, a hybrid of the flamenco and classical guitar constructions.
Many reasons have been cited for the obscurity of Western classical music in India, a country rich in its musical heritage by its own right, however the two main reasons are an utter lack of exposure and a passive disinterest in what is considered esoteric at best.
Many attempts to popularize Western classical music in India have failed in the past due to disinterest and lack of sustained efforts.
Many people have tried to find classical polynomial-time algorithms for it and failed, and therefore it is widely suspected to be outside P.
Many classical commentators such as Ibn Kathir, At-Tabari, al-Qurtubi, Suyuti, al-Undlusi ( Bahr al-Muhit ), Abu al-Fadl al-Alusi ( Ruh al-Maani ) clearly mention that verse of the Qur ' an refers to the descent of Jesus before the Day of Resurrection, indicating that Jesus would be the Sign that the Hour is close.
Many classical languages, however, use a different scheme known as quantitative metre, where patterns are based on syllable weight rather than stress.
Many well-known classical composers were also virtuoso pianists.
Many of the results of quantum mechanics are not easily visualized in terms of classical mechanics — for instance, the ground state in a quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a system, as opposed to a more " traditional " system that is thought of as simply being at rest, with zero kinetic energy.
Many systems that are treated dynamically in classical mechanics are described by such " static " wave functions.
* Many macroscopic properties of a classical system are a direct consequence of the quantum behavior of its parts.
Many of the same entropy measures in classical information theory can also be generalized to the quantum case, such as Holevo entropy and the conditional quantum entropy.
Many of his contemporaries compared his music with that of classically trained musicians, although Orbison never mentioned any classical music influences.
Many of these classical philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, particularly during the early development of classical mechanics.
" Many classical rabbis, especially Maimonides, viewed all such beliefs as a violation of Judaic principles of faith.
Many of these names appearing in the Linear B inscriptions can be found later in classical Greece like Zeus, Hera, Poseidon, Athena, Hermes, Eileithyia and Dionysos, but the etymology is the only evidence of the cults.
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