Informally, this means that arguments of this form do not give good reason to establish their conclusions, even if their premises are true.

Informally, this means that differentiable functions are very atypical among continuous functions.

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, this means that if G acts unitarily on a Hilbert space and has " almost invariant vectors ", then it has a nonzero invariant vector.

Informally, this means that the functions in the family are not exceedingly numerous or widely spread out ; rather, they stick together in a relatively " compact " manner.

Informally, lowness means that problems in B are not only solvable by machines which can solve problems in A, but are " easy to solve.

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 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, 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, given the prime factorization of m, take b to be the product of the prime factors of m that have an odd exponent ( if there are none, then take b to be 1 ).

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, a language L is in MA if for all strings in the language, there is a polynomial sized proof that Merlin can send Arthur to convince him of this fact with high probability, and for all strings not in the language there is no proof that convinces Arthur with high probability.

Informally put, the idea behind the proof of the no-trade theorem is that if there is common knowledge about the structure of a market, then any bid or offer ( i. e. attempt to initiate a trade ) will reveal the bidder's private knowledge and will be incorporated into market prices even before anyone accepts the bid or offer, so no profit will result.

Informally, an object is reachable if it is referenced by at least one variable in the program, either directly or through references from other reachable objects.

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, 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, such an object can be thought of as an assemblage of one or more chunks of rubber ( cells ), each shaped like a convex polytope, which are glued to each other by their facets — possibly with much stretching and twisting.

Informally, the RCS of an object is the cross-sectional area of a perfectly reflecting sphere that would produce the same strength reflection as would the object in question.

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, this reads as follows: something exists with the property F, there is only one such thing, and this unique thing also has the property G.

Informally, the non-commissioned officers with portepee are often called " the Feldwebel ranks " or even altogether Feldwebel, which creates a similar confusion as exists already with the word Unteroffizier.

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, w represents a " script " for the computable function f, and F represents an " interpreter " that parses the script as a prefix of its input and then executes it on the remainder of input.

Informally, the second axiom says it doesn't matter whether we restrict to W in one step or restrict first to V, then to W.

Informally, if P is any polyhedron or polytope, and tP is the polytope formed by expanding P by a factor of t in each dimension, then L ( int P, t ) is the number of integer lattice points in tP.

# From conclude: Informally, this says that if A is a theorem, then it is provable.

Informally, to estimate the area of a domain D, first pick a simple domain E whose area is easily calculated and which contains D. Now pick a sequence of random points that fall within E. Some fraction of these points will also fall within D. The area of D is then estimated as this fraction multiplied by the area of E.

Informally, if F is '= y ', G is ' is Pegasus ', and we substitute ' Pegasus ' for y, then ( 4 ) appears to allow us to infer from ' everything identical with Pegasus is Pegasus ' that something is identical with Pegasus.

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, input positions can be thought of as locations at token boundaries.

Informally we can think of elements of the Lie algebra as elements of the group that are " infinitesimally close " to the identity, and the Lie bracket is something to do with the commutator of two such infinitesimal elements.

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.

Informally, a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing his or her strategy.

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 Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values.

Informally, we can consider these products on the left hand side as being elements of the free group F =

Informally, the theorem says that the curvature of a surface can be determined entirely by measuring distances along paths on the surface.

Informally, the capacity of a classification model is related to how complicated it can be.

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.