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Informally and means
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 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, 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 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 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 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, 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 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, 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, 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, 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, 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, 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, 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.
# From conclude: Informally, this says that if A is a theorem, then it is provable.
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 G
In the mathematical field of graph theory, a spanning tree T of a connected, undirected graph G is a tree composed of all the vertices and some ( or perhaps all ) of the edges of G. Informally, a spanning tree of G is a selection of edges of G that form a tree spanning every vertex.
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, 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 and acts
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 and on
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.
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, 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, 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, the Council advises the Fijian government on every aspect of political life.
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.

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