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Formally and finite
Formally, a topological space X is called compact if each of its open covers has a finite subcover.
Formally, a set S is called finite if there exists a bijection
Formally, let S and T be finite sets and let F =
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, we start with a category C with finite products ( i. e. C has a terminal object 1 and any two objects of C have a product ).
Formally, the question of whether the universe is infinite or finite is whether it is an unbounded or bounded metric space.
Formally, an iterated function system is a finite set of contraction mappings on a complete metric space.
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 string is a finite sequence of symbols such as letters or digits.
Formally, a system is said to be observable if, for any possible sequence of state and control vectors, the current state can be determined in finite time using only the outputs ( this definition is slanted towards the state space representation ).
Formally, given a finite set X, a collection C of subsets of X, all of size n, has Property B if we can partition X into two disjoint subsets Y and Z such that every set in C meets both Y and Z.
Formally, we define a bad field as a structure of the form ( K, T ), where K is an algebraically closed field and T is an infinite, proper, distinguished subgroup of K, such that ( K, T ) is of finite Morley rank in its full language.
Formally, a deterministic finite automaton may be defined by the tuple where is the set of states of the automaton, is the set of input symbols, is the transition function that takes a state and an input symbol to a new state, is the initial state of the automaton, and is the set of accepting or final states of the automaton.
Formally, Scarf considers the following general game with a finite number of agents.
Formally, a Markov partition is used to provide a finite cover for the smooth system ; each set of the cover is associated with a single symbol, and the sequences of symbols result as a trajectory of the system moves from one of the covering sets to another.
Formally, assuming our intuition from the finite dimensional case carries over into the infinite dimensional setting, the measure should then be equal to
Formally, the upper density of a graph G is the infimum of the values α such that the finite subgraphs of G with density α have a bounded number of vertices.

Formally and game
Formally, the situation has the characteristics of a prisoner's dilemma game that is played repeatedly between the same partners, and in this case " defection "-jumping the queue-would not be advantageous.
Formally, the title of the game is just " 9 ", as shown on the box cover.
Formally, that's applying subgame perfection to solve the game.
Formally known as " Super Sloppy Slime Off ," The Big Shaboozie was the show's end game.

Formally and form
Formally, this means that the probability density functions or probability mass functions in this class have the form
Formally known as the " Six and A Half Point Pole " form, this is the second to last form of the system.
Formally incorporated in the 1890s, Shelton's municipal government is run in the Mayor / Commission form.
Formally, the singular value decomposition of an m × n real or complex matrix M is a factorization of the form
Formally, Minkowski space is a four-dimensional real vector space equipped with a nondegenerate, symmetric bilinear form with signature < tt >(−,+,+,+)</ tt > ( Some may also prefer the alternative signature < tt >(+,−,−,−)</ tt >; in general, mathematicians and general relativists prefer the former while particle physicists tend to use the latter.
" Formally, the earliest poems show the influence of conventional poetic practice, yet by The Tennis Court Oath a much more revolutionary engagement with form appears.
Formally known as trilina, the armónico has seven strings, two of which form a doubled string.
Formally, the work is a rondo, with each return of the theme appearing in varied form.
Formally a formula in the language of Peano arithmetic is a formula if it is of the form
Formally, a squeeze preserves the hyperbolic metric expressed in the form ; in a different coordinate system.
Formally, a graph rewriting system usually consists of a set of graph rewrite rules of the form, with being called pattern graph ( or left-hand side ) and being called replacement graph ( or right-hand side of the rule ).
Formally, the Barnes G-function is defined ( in the form of a Weierstrass product ) as

Formally and is
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.
Formally, a binary operation on a set S is called associative if it satisfies the associative law:
Formally, their designation is the letter Ž and the number.
Formally, the set of all context-free languages is identical to the set of languages accepted by pushdown automata ( PDA ).
Formally, the derivative of the function f at a is the limit
More rigorously, the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p. Formally,
Formally, the base is known as Naval Support Facility Diego Garcia ( the US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia ( the UK's term ).
Formally, there is a clear distinction: " DFT " refers to a mathematical transformation or function, regardless of how it is computed, whereas " FFT " refers to a specific family of algorithms for computing DFTs.
Formally, oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100 % ionic.
Formally, a bifunctor is a functor whose domain is a product category.
Formally, the system is said to have memory.
Formally, an inner product space is a vector space V over the field together with an inner product, i. e., with a map
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, when working over the reals, as here, this is accomplished by considering the limit as ε → 0 ; but the " infinitesimal " language generalizes directly to Lie groups over general rings.
Formally, a profinite group is a Hausdorff, compact, and totally disconnected topological group: that is, a topological group that is also a Stone space.
Formally, this sharing of dynamics is referred to as universality, and systems with precisely the same critical exponents are said to belong to the same universality class.
Formally, Φ = kx − ωt is the phase.

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