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case and n But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols. ( Expressed more technically, in each case the pair ( m, n ) decreases in the lexicographic order on pairs, which is a well-ordering, just like the ordering of single non-negative integers ; this means one cannot go down in the ordering infinitely many times in succession. A binary relation is the special case of an n-ary relation R ⊆ A < sub > 1 </ sub > × … × A < sub > n </ sub >, that is, a set of n-tuples where the jth component of each n-tuple is taken from the jth domain A < sub > j </ sub > of the relation. * The case n = 2 is often illustrated by saying that at any moment there is always a pair of antipodal points on the Earth's surface with equal temperatures and equal barometric pressures. For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies The properties of binomial coefficients have led to extending the meaning of the symbol beyond the basic case where n and k are nonnegative integers with ; such expressions are then still called binomial coefficients. In the case of integer order n, the function is defined by taking the limit as a non-integer α tends to n: Bennett, Bernstein, Brassard, and Vazirani proved in 1996 that a brute-force key search on a quantum computer cannot be faster than roughly 2 < sup > n / 2 </ sup > invocations of the underlying cryptographic algorithm, compared with roughly 2 < sup > n </ sup > in the classical case. Fortune's Algorithm uses a sweepline technique to achieve O ( n log n ) runtime in the planar case. If the conjecture were true, it would be a generalization of Fermat's last theorem, which could be seen as the special case n = 2: if, then. The Earley parser executes in cubic time in the general case, where n is the length of the parsed string, quadratic time for unambiguous grammars, and linear time for almost all LR ( k ) grammars. This is the use of the factor n-1 in the denominator of the formula, rather than just n. This occurs when the sample mean rather than the population mean is used to centre the data and since the sample mean is a linear combination of the data the residual to the sample mean overcounts the number of degrees of freedom by the number of constraint equations — in this case one. It is not true that if it always has been the case that a God-like being exists then a God-like being exists and it is always going to be the case that a God-like being exists in ( n ). It is not the case that a God-like being will always exist in ( n ). If G = GL < sub >*</ sub >( K ), then the set of natural numbers is a proper subset of G < sub > 0 </ sub >, since for each natural number n, there is a corresponding identity matrix of dimension n. G ( m, n ) is empty unless m = n, in which case it is the set of all nxn invertible matrices. In the case where V is of finite dimension n it is common to choose a basis for V and identify GL ( V ) with GL ( n, K ) the group of n-by-n invertible matrices on the field K.

case and = Over 99. 94 % of an atom's mass is concentrated in the nucleus ,< ref group = note > In the case of hydrogen-1, with a single electron and nucleon, the proton is, or 99. 95 % of the total atomic mass. If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field. This is not always the case: the trivial equation x = x specifies the entire plane, and the equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = 0 specifies only the single point ( 0, 0 ). If the ratio a '/ a be sufficiently constant, as is often the case, the above relation reduces to the condition of Airy, i. e. tan w '/ tan w = a constant. In the first case, ƒ ( x ) has y = c as asymptote when x tends to −∞, and in the second that ƒ ( x ) has y = c as an asymptote as x tends to +∞ Thābit's rule corresponds to the case m = n-1. Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra. a − λ1 is not invertible ( because the spectrum of a is not empty ) hence a = λ1: this algebra A is naturally isomorphic to C ( the complex case of the Gelfand-Mazur theorem ). 3-satisfiability is a special case of k-satisfiability ( k-SAT ) or simply satisfiability ( SAT ), when each clause contains exactly k = 3 literals. In the case of SWNT, covalent functionalization will break some C = C double bonds, leaving " holes " in the structure on the nanotube and, thus, modifying both its mechanical and electrical properties. Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case. Since the separation of variables in this case involves dividing by y, we must check if the constant function y = 0 is a solution of the original equation. One reason for the popularity of the dissociation constant in biochemistry and pharmacology is that in the frequently encountered case where x = y = 1, K < sub > d </ sub > has a simple physical interpretation: when = K < sub > d </ sub >, = or equivalently /(+)= 1 / 2. Consider the case when we have four layers to blend to produce the final image: F = In this case, we might compute T = A *( B * D ) only once and simply blend T * C to produce F, a single operation. In this case we may compute S = A * B once and save this result.

case and 1 The reader will find it helpful to think of the special case when the primes are of degree 1, and even more particularly, to think of the proof of Theorem 10, a special case of this theorem. Pierre-Simon Laplace and Antoine Lavoisier, in their 1780 treatise on heat, arrived at values ranging from 1, 500 to 3, 000 below the freezing-point of water, and thought that in any case it must be at least 600 below. It may be applied, as it is stated in article 1 of the convention in case of: offenses against penal law ; acts which, whether or not they are offenses, may or do jeopardize the safety of the aircraft or of persons or property therein or which jeopardize good order and discipline on board. * If the balance factor of L is + 1, a single right rotation ( with P as the root ) is needed ( Left-Left case ). Idealists are skeptics about the physical world, maintaining either: 1 ) that nothing exists outside the mind, or 2 ) that we would have no access to a mind-independent reality even if it may exist ; the latter case often takes the form of a denial of the idea that we can have unconceptualised experiences ( see Myth of the Given ). In the case of parallelization, Amdahl's law states that if P is the proportion of a program that can be made parallel ( i. e., benefit from parallelization ), and ( 1 − P ) is the proportion that cannot be parallelized ( remains serial ), then the maximum speedup that can be achieved by using N processors is A court case allowing the União do Vegetal to import and use the tea for religious purposes in the United States, Gonzales v. O Centro Espirita Beneficente Uniao do Vegetal, was heard by the U. S. Supreme Court on November 1, 2005 ; the decision, released February 21, 2006, allows the UDV to use the tea in its ceremonies pursuant to the Religious Freedom Restoration Act. On the left side of Figure 1, the case of infinite light speed is shown. Therefore, a base on balls does not increase nor decrease a player's batting average, but it does increase his on-base percentage, unless a player's on-base percentage is 1. 000, in which case it remains the same. The normal boiling point ( also called the atmospheric boiling point or the atmospheric pressure boiling point ) of a liquid is the special case in which the vapor pressure of the liquid equals the defined atmospheric pressure at sea level, 1 atmosphere. Whenever a confusion between the two kinds of definitions might arise it can be avoided by referring to the more general definition and by reintroducing the erased parameter: writing B < sub > m </ sub >( 0 ) in the first case and B < sub > m </ sub >( 1 ) in the second will unambiguously denote the value in question. In the case of the Creme Brulee, placing the ramekins in a roasting pan and filling the pan with hot water until it is 1 / 2 to 2 / 3 of the way up the sides of the ramekins transfers the heat to the custard gently, which prevents the custard from curdling. With an insurance of \$ 1, 500 promised in case of failure, Sennett also allowed Chaplin to direct his own film. As a special case, the three naturally occurring isotopes of the element hydrogen are often specified as H for < sup > 1 </ sup > H ( protium ), D for < sup > 2 </ sup > H ( deuterium ), and T for < sup > 3 </ sup > H ( tritium ). Under the federal Holidays Act, Canada Day is observed on July 1 unless that date falls on a Sunday, in which case July 2 is the statutory holiday, although celebratory events generally take place on July 1 even though it is not the legal holiday. The fastest impacts occur at more than 80 km / s in the " worst case " scenario which the asteroid hits the earth in a retrograde parabolic orbit ( because kinetic energy scales as velocity squared, earth's gravity only contributes 1 km / s to this figure, not 11 km / s ). Since these stock additions retain the short pistol barrel ( as short as 100 mm ( 4 inches )) they are highly restricted under the NFA unless the shoulder stocks are of original manufacture for the gun and the gun has been " delisted " as outlined in links 1 & 2 in the paragraph above, as is the case with so-equipped " Broomhandle " Mausers and Lugers. In this case, the ordinals 0, 1,,, and are regular, whereas 2, 3,, and ω < sub > ω · 2 </ sub > are initial ordinals which are not regular. Most canids bear young once a year, from 1 to 16 or more ( in the case of the African wild dog ) at a time.

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