Formally, dependence refers to any situation in which random variables do not satisfy a mathematical condition of probabilistic independence.

Formally, a topological space X is called compact if each of its open covers has a finite subcover.

Formally, one has an implication, not an equivalence, so the solution set may get larger.

Formally the " head of state " can also personally be the " head of government " ( ex officio or by ad hoc cumulation such as an absolute monarch nominating himself ) but otherwise has formal precedence over the Head of Government and other ministers, whether he is their actual political superior ( absolute monarch, executive president ) or rather theoretical or ceremonial in character.

Formally described as " Truck, Cargo: 10-Ton, 8x8 ", it has been nicknamed the " Dragon Wagon ".

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 it is a part of Novosibirsk city, and has never been a closed city.

Formally, DFS is an uninformed search that progresses by expanding the first child node of the search tree that appears and thus going deeper and deeper until a goal node is found, or until it hits a node that has no children.

Informally, G has the above presentation if it is the " freest group " generated by S subject only to the relations R. Formally, the group G is said to have the above presentation if it is isomorphic to the quotient of a free group on S by the normal subgroup generated by the relations R.

It has been leased from the National Trust since 1974 by the Somerset Wildlife Trust ( Formally Somerset Trust for Nature Conservation ) and is run as a nature reserve and visitor centre.

Formally known as trilina, the armónico has seven strings, two of which form a doubled string.

Formally known as Bootle-cum-Linacre, the town is < span style =" white-space: nowrap "> 4 miles ( 6. 4 km )</ span > to the north of Liverpool city centre, and has a total resident population of 77, 640.

Formally, this means that, for some function f, the image f ( D ) of a directed set D ( i. e. the set of the images of each element of D ) is again directed and has as a least upper bound the image of the least upper bound of D. One could also say that f preserves directed suprema.

Following a merger with the Furnishing Industry Trust ( Formally The Furnishing Trades Benevolent Association ) in 2011, the Company has become the most significant charity in the sector, supporting the needy and promoting welfare and education of those entering and working within the industry, as well as the wider support of the charitable work of the Mayoralty and the Corporation of the City of London.

Formally established in 1475, though in fact much older, it has 75, 000 codices from throughout history.

Formally, if R is a Noetherian ring and I is a principal, proper ideal of R, then I has height at most one.

* Formally real field, an algebraic field that has the so-called " real " property

Formally, a deterministic algorithm computes a mathematical function ; a function has a unique value for any given input, and the algorithm is a process that produces this particular value as output.

Formally, an antihomomorphism between X and Y is a homomorphism, where equals Y as a set, but has multiplication reversed: denoting the multiplication on Y as and the multiplication on as, we have.

Formally, given two partially ordered sets ( S, ≤) and ( T, ≤), a function f: S → T is an order-embedding if f is both order-preserving and order-reflecting, i. e. for all x and y in S, one has

Formally described in Stephen Gilligan's article: The relational self: the expanding of love beyond desire ( 1996 ), and expanded on in his book: The Courage to Love ( 1997 ), it has become a major new approach in psychotherapy and healing.

Formally launched in 2004, the network currently has 16 members in nine states.

Enbridge currently has offices in Enbridge Place ( Formally ING Tower ), Manulife Place, and Royal Bank Building.

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 named " Olallie ", it has usually been marketed as olallieberry, just as " Marion " is sold as marionberry.

Formally, the verbal noun ( VN, still retaining verbal characteristics ) takes okurigana, as is usual for verbs, while the deverbal noun ( DVN, without verbal characteristics ) does not take okurigana, as is usual for nouns.

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, the title of the game is just " 9 ", as shown on the box cover.

Formally, Scarf considers the following general game with a finite number of agents.

Formally, a finite game in extensive form is a structure

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 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, a set S is called finite if there exists a bijection

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, a frame is defined to be a lattice L in which finite meets distribute over arbitrary joins, i. e. every ( even infinite ) subset

Formally, Φ = kx − ωt is the phase.