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Informally and given
Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin.
Informally recognised for over a century as a convention of the constitution, the position of Leader of the Opposition was given statutory recognition in 1937 by the Ministers of the Crown Act.
Informally, this means that given a constructive proof that an object exists, then that constructive proof can be turned into an algorithm for generating an example of it.
Informally, these theorems say that given more time, a Turing machine can solve more problems.
Informally, senators are sometimes given the higher title of ' Venerable '.
Informally, the terms C standard library or C library or libc are also used to designate a particular implementation on a given system.
Informally, the theorem says that given some formal arithmetic, the concept of truth in that arithmetic is not definable using the expressive means that arithmetic affords.
Informally, given a problem, the Turing jump returns the set of Turing machines which halt when given access to an oracle that solves that problem.
Informally, the function type refers to the set of functions that, given an input of type, produce an output of type.
Informally, hypoxemic hypoxia is sometimes informally given as hypoxic hypoxia.
Informally, this means that whenever we are given the unit ball of some seminorm, we can find a " much smaller " unit ball of another seminorm inside it, or that any neighborhood of 0 contains a " much smaller " neighborhood.

Informally and prime
Informally speaking, the prime number theorem states that if a random integer is selected in the range of zero to some large integer N, the probability that the selected integer is prime is about 1 / ln ( N ), where ln ( N ) is the natural logarithm of N. For example, among the positive integers up to and including N = 10 < sup > 3 </ sup > about one in seven numbers is prime, whereas up to and including N = 10 < sup > 10 </ sup > about one in 23 numbers is prime ( where ln ( 10 < sup > 3 </ sup >)= 6. 90775528. and ln ( 10 < sup > 10 </ sup >)= 23. 0258509 ).
Informally it solves the following problem: Given an integer N, find its prime factors.

Informally and take
Informally known as " The Big Book " ( with its first 164 pages virtually unchanged since the 1939 edition ), it suggests a twelve-step program in which members admit that they are powerless over alcohol and need help from a " higher power "; seek guidance and strength through prayer and meditation from God or Higher Power of their own understanding ; take a moral inventory with care to include resentments ; list and become ready to remove character defects ; list and make amends to those harmed, and then try to help other alcoholics recover.
Informally, however, scientists may still take advantage of the pathetic fallacy for quick and convenient metaphoric explanations of complex scientific concepts in a readily understood way.

Informally and b
Informally, two sequences ( a < sub > n </ sub >) and ( b < sub > n </ sub >) become closer and closer if and only if more and more of their terms agree exactly.

Informally and be
Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
Informally, the theorem says that the curvature of a surface can be determined entirely by measuring angles and distances on the surface.
Such a definition can be formulated in terms of equivalence classes of smooth functions on M. Informally, we will say that two smooth functions f and g are equivalent at a point x if they have the same first-order behavior near x.
Informally the Church – Turing thesis states that if some method ( algorithm ) exists to carry out a calculation, then the same calculation can also be carried out by a Turing machine ( as well as by a recursively definable function, and by a λ-function ).
( Informally, input positions can be thought of as locations at token boundaries.
Informally, he may have been known as " Dickon ", according to a sixteenth-century legend of a note, warning of treachery, that was sent to the Duke of Norfolk on the eve of Bosworth: " Jack of Norffolke be not to bolde ,/ For Dyckon thy maister is bought and solde ".
Informally, the " P vs. NP " question asks whether every optimization problem whose answers can be efficiently verified for correctness / optimality can be solved optimally with an efficient algorithm.
Informally, a conservative force can be thought of as a force that conserves mechanical energy.
In other words, L can be solved in polynomial time by an oracle machine with an oracle for H. Informally, we can think of an algorithm that can call such an oracle machine as a subroutine for solving H, and solves L in polynomial time, if the subroutine call takes only one step to compute.
Informally, the theorem says that the curvature of a surface can be determined entirely by measuring distances along paths on the surface.
Informally, a set of natural numbers A is Turing reducible to a set B if there is an oracle machine that correctly tells whether numbers are in A when run with B as the oracle set ( in this case, the set A is also said to be ( relatively ) computable from B and recursive in B ).
Informally, the name " NFL Europe " continued to be used in the United States, including for the league's English-language Web site, nfleurope. com.
Informally this has been called the " Step Boundary ", although the step-like shape of the boundary was not apparent for several decades — the source of the Arkansas, believed to be near the 42nd parallel, was not known until John C. Frémont located it in the 1840s, hundreds of miles south of the 42nd parallel.
Informally, free abelian groups or formal sums may also be seen as signed multisets with elements in B.
Informally, dogs may be studied by those with no specific scientific training, such as publicists and authors, breeders, trainers, police dog handlers, animal communicators and others, through literature, history, and personal experience.
Informally, the capacity of a classification model is related to how complicated it can be.
Informally, a free object over a set A can be thought as being a " generic " algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.
Informally, C can be regarded as the *- algebra of continuous complex-valued functions over the compact matrix quantum group, and u can be regarded as a finite-dimensional representation of the compact matrix quantum group.
Informally it can be considered more widely: from a post-colonial form of amical protection, or protectorate, to confederation of unequal members when the lesser partner ( s ) delegate to the major one ( often the former colonial power ) some authority normally exclusively retained by a self-governing state, often in such fields as defence and foreign relations, while often enjoying favorable economic terms such as market access.
Informally, eigenfaces can be considered a set of " standardized face ingredients ", derived from statistical analysis of many pictures of faces.
Informally, subvarieties are in general position if they cannot be described more simply than others.

Informally and have
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.
Informally, they require human practices to sustain their existence, but they have an effect that is ( basically ) universally agreed upon.
Informally, two crystals tend to be in the same crystal system if they have similar symmetries, though there are many exceptions to this.
Informally, a thick object in our space is simply connected if it consists of one piece and does not have any " holes " that pass all the way through it.
Informally, this type of graph is a set of objects called vertices ( or nodes ) connected by links called edges ( or arcs ), which can also have associated directions.
Informally, the Houston Cougars have also been referred to as the Coogs, UH, or simply Houston.
Informally, it says that all sufficiently long words in a regular language may be pumped — that is, have a middle section of the word repeated an arbitrary number of times — to produce a new word which also lies within the same language.

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