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 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, the theorem states that arithmetical truth cannot be defined in arithmetic.

" Informally, hypothesis boosting problem asks whether an efficient learning algorithm that outputs an hypothesis whose performance is only slightly better than random guessing a weak learner implies the existence of an efficient algorithm that outputs an hypothesis of arbitrary accuracy a strong learner.

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, 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, in attempting to estimate the causal effect of some variable x on another y, an instrument is a third variable z which affects y only through its effect on x.

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, 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, a Euclidean plane isometry is any way of transforming the plane without " deforming " it.

Informally, a strategy for a player is a way of playing in which his plays are entirely determined by the foregoing plays.

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

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.

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, 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, 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, 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, a loss of $ 1 million or more on this portfolio is expected on 1 day in 20.

Informally, a skein relation gives a linear relation between the values of a knot polynomial on a collection of three links which differ from each other only in a small region.

Informally, the terms C standard library or C library or libc are also used to designate a particular implementation on a given system.

Informally, a loop invariant is a statement of the conditions that should be true on entry into a loop and that are guaranteed to remain true on every iteration of the loop.

Informally stated, with certain technical assumptions, every representation of the Heisenberg group is equivalent to the position operators and momentum operators on R < sup > n </ sup >.

Informally, the Council advises the Fijian government on every aspect of political life.

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, many Mechlinians ( in Dutch Mechelaars and locally pronounced Mecheleirs, people from this city ) daily speak Mechlinian ( in Dutch as well as locally Mechels ), a dialect by Dutch-speakers of Belgium pin-pointingly distincted from other Brabantic dialects by three different vowels of Dutch ( as in zout or rauw, in kei or bijl, in nu ) being typically pronounced as a same vowel – close to the one in English ' raw ' which does not appear in other dialects of the Flemish Region or in standard Dutch.

Informally speaking, a step function is a piecewise constant function having only finitely many pieces.

Informally, eigenfaces can be considered a set of " standardized face ingredients ", derived from statistical analysis of many pictures of faces.

Informally, two crystals tend to be in the same crystal system if they have similar symmetries, though there are many exceptions to this.

Informally, many older Lossos stated that the Nawdba came " from the East, toward Djougou ( in Bénin ).

Informally, this is true because a polynomial-time algorithm can make polynomially many queries to other polynomial-time algorithms, retaining its polynomial running time.

Informally, the market spilled into the surrounding neighborhood, both in terms of street vendors and in terms of the nearby Magazin Universal (" Universal Store ") named Bucur Obor, a large commercial building that has been parcelled up into hundreds of small, independent retail stores.

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, 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, any GPS navigation device, especially an automotive navigation system

Informally, and primarily in fiction, a detective is any licensed or unlicensed person who solves crimes, including historical crimes, or looks into records.

Informally, the term is often applied in a joking manner to describe any horse that acts up and bucks with or without a rider.

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.

Informally, any sloping line is called diagonal.

Informally, software developers may also use zeroise to mean any overwriting of sensitive data, not necessarily of a cryptographic nature.

: 4: Informally, any whaler of any size or any vessel engaged in whale watching.

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, the following titles of nobility, and any holders thereof:

Informally, it says that any " nice looking " shape without holes can be smoothly deformed into a disk.