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Page "Inverse element" ¶ 22
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By and contrast
By contrast, the energetic reaction of the leader to the full demands his decision imposes upon him strengthens the moral intuition and gives us the measure of the man.
By contrast, even experienced linguists commonly know no more of the range of possibilities in tone systems than the over-simple distinction between register and contour languages.
By contrast, a good deal of nuclear pacifism begins with the contingencies and the probabilities, and not with the moral nature of the action to be done ; ;
By contrast, the National Union Party was united and energized as Lincoln made emancipation the central issue, and state Republican parties stressed the perfidy of the Copperheads.
By contrast, the cursive developed out of the Nabataean alphabet in the same period soon became the standard for writing Arabic, evolving into the Arabic alphabet as it stood by the time of the early spread of Islam.
has no zero in F. By contrast, the fundamental theorem of algebra states that the field of complex numbers is algebraically closed.
By contrast, the Rijndael specification per se is specified with block and key sizes that may be any multiple of 32 bits, both with a minimum of 128 and a maximum of 256 bits.
The largest species are red alder ( A. rubra ) on the west coast of North America, and black alder ( A. glutinosa ), native to most of Europe and widely introduced elsewhere, both reaching over 30 m. By contrast, the widespread Alnus viridis ( green alder ) is rarely more than a 5 m tall shrub.
By the standards of 19th century tycoons, Carnegie was not a particularly ruthless man but a humanitarian with enough acquisitiveness to go in the ruthless pursuit of money ; on the other hand, the contrast between his life and the lives of many of his own workers and of the poor, in general, was stark.
By contrast, Kabbalism assumed an " eternal Torah " which was not identical to the Torah written in Hebrew.
By contrast, while defendants in most civil law systems can be compelled to give a statement, this statement is not subject to cross-examination by the prosecutor and not given under oath.
By contrast, in an inquisitiorial system, the fact that the defendant has confessed is merely one more fact that is entered into evidence, and a confession by the defendant does not remove the requirement that the prosecution present a full case.
By contrast, Tom Wolfe's Bonfire of the Vanities ( 1987 ) portrays a wealthy, white protagonist, Sherman McCoy, getting lost off the Major Deegan Expressway in the South Bronx and having an altercation with locals.
By contrast, in mainstream Analytical philosophy the topic is more confined to abstract investigation, in the work of such influential theorists as W. V. O. Quine, to name one of many.
By contrast, substance theory explains the compresence of properties by asserting that the properties are found together because it is the substance that has those properties.
By contrast, evidence based on the textual differences between the Septuagint and the Masoretic Text has been used to argue that the context of the MT truly does depict a historical Jeremiah.
By contrast most of the party's seats were won either due to the absence of a candidate from one of the other parties or in rural areas on the " Celtic fringe ", where local evidence suggests that economic ideas were at best peripheral to the electorate's concerns.
By contrast, the normal vaginal discharge will vary in consistency and amount throughout the menstrual cycle and is at its clearest at ovulation-about 2 weeks before the period starts.
By contrast, the British press were jubilant ; many newspapers sought to portray the battle as a victory for Britain over anarchy, and the success was used to attack the supposedly pro-republican Whig politicians Charles James Fox and Richard Brinsley Sheridan.
By contrast, in civil law jurisdictions ( the legal tradition that prevails in, or is combined with common law in, Europe and most non-Islamic, non-common law countries ), courts lack authority to act where there is no statute, and judicial precedent is given less interpretive weight ( which means that a judge deciding a given case has more freedom to interpret the text of a statute independently, and less predictably ), and scholarly literature is given more.
By contrast to statutory codification of common law, some statutes displace common law, for example to create a new cause of action that did not exist in the common law, or to legislatively overrule the common law.
By contrast, a hard conversion or an adaptive conversion may not be exactly equivalent.
" By contrast, the composition from the Byzantine point of view portrays Constantine Palaeologus as a brave leader who gave his life for the cause.
By contrast, in ceremonial monarchies, the monarch holds little actual power or direct political influence.
By contrast, Liechtenstein and Monaco are considered democratic states, yet the ruling monarchs in these countries wield significant executive power.

By and zero
By international agreement, absolute zero is defined as on the Kelvin scale and as − 273. 15 ° on the Celsius scale.
By filling the character pointer memory with values from zero to 1919 this essentially turned the text mode display into a very high resolution graphics mode, with the " font memory ", acting as the high resolution Raster graphics video memory.
At standard temperature, pressure and concentration conditions, the cell's emf ( measured by a multimeter ) is 0. 34 V. By definition, the electrode potential for the SHE is zero.
By convention, one of these, the Prime Meridian, which passes through the Royal Observatory, Greenwich, England, establishes the position of zero degrees longitude.
By lowering the temperature, the fraction of the superfluid density increases from zero at T < sub > λ </ sub > to one at zero kelvin.
By Newton's first law, this situation implies that the net force and net torque ( also known as moment of force ) on every part of the system is zero.
By setting the index bar to zero, the sun can be viewed through the telescope.
By this date the Earth sensor brightness indication had essentially gone to zero, however, this time telemetry data indicated the Earth-brightness measurement had increased to the nominal value for that point in the trajectory.
By convention, area 0 ( zero ) or < tt > 0. 0. 0. 0 </ tt > represents the core or backbone region of an OSPF network.
By selecting the witness as a random string, the verifier is a probabilistic polynomial-time Turing Machine whose probability of accepting x when x is in X is large ( greater than 1 / 2, say ), but zero if x is not in X ( for RP ); of rejecting x when x is not in X is large but zero if x is in X ( for co-RP ); and of correctly accepting or rejecting x as a member of X is large, but zero of incorrectly accepting or rejecting x ( for ZPP ).
By measuring the beam current it could be determined whether the spot was originally a zero or a one, and a new value could be stored by the beam.
By the time of the 2000 Census, the town shows a population of zero, and much of it appears to have been annexed into the city of Sylacauga.
By contrast, between 2007 and 2010, the OCC and OTS combined made ' zero ' criminal referrals ; Black concluded that elite financial fraud has effectively been decriminalized.
By filling the underflow gap like this, significant digits are lost, but not to the extent as when doing flush to zero on underflow ( losing all significant digits all through the underflow gap ).
By the 7th century CE Indian mathematicians were familiar enough with the notion of infinity as to define it as the quantity whose denominator is zero.
By changing the reference frame one can set the linear momentum and position to zero and orient the spin angular momentum along the positive z axis.
By Ampère's law, we know that the line integral of B ( the magnetic flux density vector ) around this loop is zero, since it encloses no electrical currents ( it can be also assumed that the circuital electric field passing through the loop is constant under such conditions: a constant or constantly changing current through the solenoid ).
By Kolmogorov's zero-one law, for any given p, the probability that an infinite cluster exists is either zero or one.
By 935 seconds after the retrofire, the cabin pressure was zero, and remained there until the capsule hit the Earth's atmosphere.
By the law of large numbers, goes to zero as n approaches infinity, and by the joint Asymptotic Equipartition Property the same applies to.

0.197 seconds.