Informally, Nakayama's lemma says that one can still regard a coherent sheaf as coming from a vector bundle in some sense.

Informally, the Ricci flow tends to expand negatively curved regions of the manifold, and contract positively curved regions.

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 case of a point charge in an arbitrary static electric field is a simple consequence of Gauss's law.

Informally, other members of the higher hierarchic echelons of the Catholic Church are in recent times also occasionally called " Princes of the church ", in which case this title may occasionally carry ironic connotations.

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, 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, 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, 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, word formation rules form " new words " ( that is, new lexemes ), while inflection rules yield variant forms of the " same " word ( lexeme ).

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, 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.

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

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.

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 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, by extension, the line generated by a basis vector in linear algebra

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

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, the center of mass ( and center of gravity in a uniform gravitational field ) is the average of all points, weighted by the local density or specific weight.

Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs.

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, these conditions state that the dual of a statement is formed by reversing arrows and compositions.

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, a soundness theorem for a deductive system expresses that all provable sentences are true.

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, criticism is a common aspect of all human expression and need not necessarily imply skilled or accurate expressions of judgment.

Informally, it is the " average " ( arithmetic mean ) of all points of X.

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, 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.

In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace W of a vector space V equipped with a bilinear form B is the set W < sup >⊥</ sup > of all vectors in V that are orthogonal to every vector in W. Informally, it is called the perp, short for perpendicular complement.

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.