Since C is rational, this correspondence has K coincidences, each of which implies a line of the pencil which meets its image.

Since they are produced automatically without any rational analysis and verification ( see the modern idea of the subconscious ) of whether they are correct or not, they need to be confirmed ( epimarteresis: confirmation ), a process which must follow each assumption.

Since the field of constructible points is closed under square roots, it contains all points that can be obtained by a finite sequence of quadratic extensions of the field of complex numbers with rational coefficients.

When objectively analyzing the condition for learning Gagné says: “ Since the purpose of instruction is learning, the central focus for rational derivation of instructional techniques is the human learner.

Since considerations of the physical details of actions are necessarily bound up with a person's subjective preferences, and could have been brought about without the action of a rational will, Kant concluded that the expected consequences of an act are themselves morally neutral, and therefore irrelevant to moral deliberation.

Justice Rehnquist echoed this point in his opinion in United States v. Lopez, stating: Since ( Wickard ), the Court has ... undertaken to decide whether a rational basis existed for concluding that a regulated activity sufficiently affected interstate commerce.

Since S is non-empty, there is a rational number L such that L < s for some s in S. Now define sequences of rationals ( u < sub > n </ sub >) and ( l < sub > n </ sub >) as follows:

Since √ 2 is a real number, which can be either rational or irrational, the only option left is for √ 2 to be irrational.

Since for even s the Riemann zeta function has an analytic expression in terms of a rational multiple of, then for even exponents, this infinite product evaluates to a rational number.

Since the first coefficient a < sub > 0 </ sub > of the continued fraction of x plays no role in Khinchin's theorem and since the rational numbers have Lebesgue measure zero, we are reduced to the study of irrational numbers in the unit interval, i. e., those in.

Since all the inputs are rational or integer the result is:

Since the paradox assumes the ass will always go to whichever is closer, it will die of both hunger and thirst since it cannot make any rational decision to choose one over the other.

“ Since parties aim at such goals as getting their programs developed or accepted and getting positions of influence within organizations, it is clear that they operate only within a rational order within which these goals are possible to attain and only when there is a struggle for power ” ( Hurst 206 )

Since the ratio of coefficients is a rational function, the power series can be written as a generalized hypergeometric series.

Since the payoffs for some amount of cooperation in the Centipede game are so much larger than immediate defection, the " rational " solutions given by backward induction can seem paradoxical.

Since 1897 he had run the Wissenschaftlich-humanitäres Komitee (" Scientific-Humanitarian Committee "), which campaigned on conservative and rational grounds for gay rights and tolerance.

Since it was possible to incorporate the rational expectations hypothesis into macroeconomic models whilst avoiding the stark conclusions that Sargent and Wallace reached, the policy-ineffectiveness proposition has had less of a lasting impact on macroeconomic reality than first may have been expected.

Since − i is algebraic, but certainly not rational, e < sup > π </ sup > is transcendental.

As Matthew Simon writes, “ Since it served as a fundamental concept, not only in physiology but also in pathology and therapy, complexion theory provided important support for the idea that medicine constituted a unified and rational body of knowledge .” By observation and judgment, medieval physicians determined the proper complexion of the individual when healthy.

Since World War II, the Foundation has devoted its efforts to strengthening the social sciences as a means of achieving more informed and rational social policy.

Since it has only a tiny fraction of its parent's radius ( and therefore its moment of inertia is sharply reduced ), a neutron star is formed with very high rotation speed, and then gradually slows down.

Since the early 2000s, this rule was changed by the FEI so that each second or fraction of a second over the time allowed would result in 1 time penalty ( e. g. with a time allowed of 72 seconds, a time of 73. 09 seconds would result in 2 time faults ).

Since the dielectric strength of gases varies depending on the shape and configuration of the electrodes, it is usually measured as a fraction of the dielectric strength of Nitrogen gas.

Since a single integrated circuit can provide a complete phase-locked-loop building block, the technique is widely used in modern electronic devices, with output frequencies from a fraction of a hertz up to many gigahertz.

Since specific gene therapies cannot readily be used to treat a significant fraction of patients with retinal dystrophy, there is a major interest in developing a more generally applicable survival factor therapy.

Since the notes ring for some significant fraction of a second when struck with the damper pad up, and ringing bars do not stop ringing immediately when contacted by the pad, a technique called " after pedaling " is necessary.

Since then, a fraction of dissident peronists allied with conservative PRO, Julio Cobos-through Federal Consensus ( ConFe )- started negotiations with his former party, UCR.

Since the reaction wheel is a small fraction of the spacecraft's total mass, easily-measurable changes in its speed provide very precise changes in angle.

Since carbide makes up a large fraction of the material, white cast iron could reasonably be classified as a cermet.

Since 1996, the head coaches for the two All-Star teams have been the coaches of the two teams that are leading their respective conferences in point percentage ( i. e. fraction of points obtained out of total possible points ).

Since rocket delta-v has a non linear relationship to mass fraction due to the rocket equation, any small reduction in delta-v gives a relatively large reduction in the required mass fraction ; and starting a mission at higher altitude also helps.

Since the deposit ( usually one or more coins ) is a fraction of the bike's cost, this does little to deter theft.

Since high frequency corresponds to electrolyte activities, while low frequencies corresponds to electrodes process, it can be deduced that only a small fraction of the overall resistance is from the electrolyte and most resistance comes from anode and cathode.

Since the November 2005 city elections, three prominent Social Democrats have left their fraction: Winnie Berndtson, Finn Rudaizky and Winnie Larsen-Jensen.

Since this is a quadratic irrational, the continued fraction must be periodic ( unless n is square, in which case the factorization is obvious ).

Since there are hundreds or even thousands of mtDNA copies in every eukaryotic cell, mutations may either be present in all copies ( homoplasmy ) or affect only a fraction of them ( heteroplasmy ).

Since UE ’ s founding, its constitution has limited the pay of its officers to “ a salary not to exceed the highest weekly wage paid in the industry .” Linked to the pay rates of production workers at GE, the annual salaries of UE ’ s three national officers are currently $ 62, 072 – a fraction of what other unions pay their officers.

Since the fraction of the reactant population that will break down in each time period can be expressed as:

Since audience numbers in the Interest and Desire phase of the AIDA sales model narrow down to a fraction of the Awareness audience, the line could be drawn right below the awareness set of activities.

Since only a fraction of the recapitalization would be listed as debt on the balance sheet, hybrids allowed companies to repurchase more shares than previously without negatively affecting their credit rating.

Since all but a tiny fraction of real estate transactions close on a date other than this one specified annual date, most transactions must include an adjustment to assure that both the seller and the buyer end up paying their share of the annual property tax, proportionate to the percentage of the year that each has ownership of the property.

Since nuclear fuel is used for several years ( burnup ) in a nuclear power plant, the final amount of < sup > 151 </ sup > Sm in the spent nuclear fuel at discharge is only a small fraction of the total < sup > 151 </ sup > Sm produced during the use of the fuel.