 Page "Structural induction" ¶ 1
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Formally and speaking Formally speaking, a collation method typically defines a total order on a set of possible identifiers, called sort keys, which consequently produces a total preorder on the set of items of information ( items with the same identifier are not placed in any defined order ). Formally speaking, the strategy pattern defines a family of algorithms, encapsulates each one, and makes them interchangeable. Formally speaking, the opportunity was extended to all classes to join China's project on its Leninist terms. Formally speaking, the curves must be differentiable curves in the Euclidean plane.

Formally and then Formally, if d is the dimension of the parameter, and n is the number of samples, if as and as, then the model is semi-parametric. Formally, if is an open subset of the complex plane, a point of, and is a holomorphic function, then is called a removable singularity for if there exists a holomorphic function which coincides with on. Formally declared on October 9, 1970, the Khmer Republic was a right-wing pro-United States military-led government headed by General Lon Nol and Prince Sisowath Sirik Matak that took power in the March 18, 1970 coup against Prince Norodom Sihanouk, then the country's head of state. Formally, if we write F < sub > Δ </ sub >( x ) to mean the f-polynomial of Δ, then the h-polynomial of Δ is * General Headquarters United Nations Command ( Korea ) ( UNC ) — Formally activated 10 July 1950, before then Allied forces were formally under American operational control. Formally it consists of three groups of four measure phrases of three to four chords repeated four times each, ABC :|| ABC, which then merges with the next movement, " Floe " with the entrance of the horns. Formally, if T is a complete sufficient statistic for θ and E ( g ( T )) = τ ( θ ) then g ( T ) is the minimum-variance unbiased estimator ( MVUE ) of τ ( θ ). Formally, if R is a Noetherian ring and I is a principal, proper ideal of R, then I has height at most one. Formally, given a partially ordered set ( P, ≤), then an element g of a subset S of P is the greatest element of S if Formally, define the set of lines in the plane P as L ( P ); then a rigid motion of the plane takes lines to lines – the group of rigid motions acts on the set of lines – and one may ask which lines are unchanged by an action. Formally, if is a limit ordinal, then a set is closed in if and only if for every < math > Formally, if f is a harmonic function, then f cannot exhibit a true local maximum within the domain of definition of f. In other words, either f is a constant function, or, for any point inside the domain of f, there exist other points arbitrarily close to at which f takes larger values. Formally, if we denote the set of stable functions by S ( D ) and the stability radius by r ( f, D ), then: Formally, assuming our intuition from the finite dimensional case carries over into the infinite dimensional setting, the measure should then be equal to

Formally and satisfies Formally, a binary operation on a set S is called associative if it satisfies the associative law: Formally, if M is a set, the identity function f on M is defined to be that function with domain and codomain M which satisfies Formally we mean that is an ideal if it satisfies the following conditions: Formally, a Lie superalgebra is a ( nonassociative ) Z < sub > 2 </ sub >- graded algebra, or superalgebra, over a commutative ring ( typically R or C ) whose product, called the Lie superbracket or supercommutator, satisfies the two conditions ( analogs of the usual Lie algebra axioms, with grading ): Formally, the game ( coalitional game ) consists of a finite set of players, called the grand coalition, and a characteristic function denotes the power set of .</ ref > from the set of all possible coalitions of players to a set of payments that satisfies. Formally, a biased graph Ω is a pair ( G, B ) where B is a linear class of circles ; this by definition is a class of circles that satisfies the theta-graph property mentioned above.

Formally and axiom Formally, assuming the axiom of choice, cardinality of a set X is the least ordinal α such that there is a bijection between X and α.

Formally and which Formally organized vocational programs supported by federal funds allow high school students to gain experience in a field of work which is likely to lead to a full-time job on graduation. However, shortly after this positive result, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems ( 1931 ), showing that in any sufficiently strong axiomatic system there are true statements which cannot be proved in the system. Formally, a frame is defined to be a lattice L in which finite meets distribute over arbitrary joins, i. e. every ( even infinite ) subset Formally, collective noun forms such as “ a group of people ” are represented by second-order variables, or by first-order variables standing for sets ( which are well-defined objects in mathematics and logic ). Formally, a detailed balanced process is the one on which the probability to be in the state x and transit to x ' must be the same as to be in the state x ' and transit to x. Formally, the sequence of partial sums of some infinite summation converges if for every fixed power of X the coefficient stabilizes: there is a point beyond which all further partial sums have the same coefficient. Formally, a unique factorization domain is defined to be an integral domain R in which every non-zero and non-unit x of R can be written as a product ( including an empty product ) of irreducible elements p < sub > i </ sub > of R and a unit u: Formally, an elliptic function is a function meromorphic on for which there exist two non-zero complex numbers and with ( in other words, not parallel ), such that and for all. In late 1900s the day that of the City was founded is Jakin School is a Private School is Formally Part of Jakin School Board was Grades One through Twelve there is no Football field on this school. In 1966 When Jakin School was Closed were Sent to Blakely-Union Elementary, Junior High, and High School ( which later Became Early County High, Middle, and Elementary School ). while Carver school was built for African-American students grades One through Twelve. although late 1960s when Carver school was closed along with Kestler School was based in Damascus were sent to Washington High & Elementary at Blakely. In addition to small farm agriculture, Jakin's early economic growth resulted from turpentine. Formally, dependence refers to any situation in which random variables do not satisfy a mathematical condition of probabilistic independence. Formally, let P be an expression in which the variable x is free. Formally, a statistic s is a measurable function of X ; thus, a statistic s is evaluated on a random variable X, taking the value s ( X ), which is itself a random variable. Formally, this follows from the convolution theorem in mathematics, which relates the Fourier transform of the power spectrum ( the intensity of each frequency ) to its autocorrelation. Formally, it is anything which when offered in payment extinguishes the debt. Formally known as trilina, the armónico has seven strings, two of which form a doubled string. Formally, let f: < sup > n </ sup > → be the cost function which must be minimized. Formally known as Motion Picture Distribution LP, it was re branded and relaunched in 2007 due to the break-up of its preceding company, Alliance Atlantis, which was sold off piece by piece to Canwest Global, GS Capital Partners, along with several other smaller companies. Formally, a rigged Hilbert space consists of a Hilbert space H, together with a subspace Φ which carries a finer topology, that is one for which the natural inclusion Formally known as the Inverurie Parish Church, a split in Church of Scotland over the appointment of ministers in 1843 ( The Disruption ) led to the creation of the West Parish Church ( known locally as " The West Kirk ") which was founded as a Free Church ( a church free from Edinburgh control ) thus causing the Inverurie Parish Church to change its name.

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