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Informally and speaking
Informally speaking, a step function is a piecewise constant function having only finitely many pieces.
Informally speaking, every matrix satisfies its own characteristic equation.
Informally speaking, continuations can account for the similarity between such sentences as " Alice sees Bob "— formally,and " Alice sees everyone ", i. e..

Informally and prime
Informally it solves the following problem: Given an integer N, find its prime factors.
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 and number
Informally basis vectors are like " building blocks of a vector ", they are added together to make a vector, and the coordinates are the number of basis vectors in each direction.
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, the kth Betti number refers to the number of unconnected k-dimensional surfaces.
Informally, the Levenshtein distance between two words is equal to the number of single-character edits required to change one word into the other.
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.

Informally and theorem
Informally, the theorem says that the curvature of a surface can be determined entirely by measuring angles and distances on the surface.
Informally, a soundness theorem for a deductive system expresses that all provable sentences are true.
Informally, the theorem says that the curvature of a surface can be determined entirely by measuring distances along paths on the surface.
Informally, the theorem states that arithmetical truth cannot be defined in arithmetic.
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.
# From conclude: Informally, this says that if A is a theorem, then it is provable.
Informally, Marcinkiewicz's theorem is
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 and states
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, it states that " A random variable that depends in a Lipschitz way on many independent variables ( but not too much on any of them ) is essentially constant ".

Informally and if
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, 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 relational database table is often described as " normalized " if it is in the Third Normal Form.
Informally, a graph is a good expander if it has low degree and high expansion parameters.
Informally, a measure has the property of being monotone function | monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B.
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, 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, 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, this means that arguments of this form do not give good reason to establish their conclusions, even if their premises are true.
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, subvarieties are in general position if they cannot be described more simply than others.
Informally, A probabilistically causes B if As occurrence increases the probability of B.
Informally, two sets are close in the Hausdorff distance if every point of either set is close to some point of the other set.
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, 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 and random
" 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 and is
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, it is a permutation of the group elements such that the structure remains unchanged.
Informally, it is the similarity between observations as a function of the time separation between them.
Informally, this is true because polynomial time algorithms are closed under composition.
Informally, Kajang is known as the " Satay Town ", and is famous among tourists and locals alike.
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, word formation rules form " new words " ( that is, new lexemes ), while inflection rules yield variant forms of the " same " word ( lexeme ).
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 word is also used to describe a procedure or process with a specific purpose.
Informally, a permutation of a set of objects is an arrangement of those objects into a particular order.

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