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

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, this type of graph is a set of objects called vertices ( or nodes ) connected by links called edges ( or arcs ), which can also have associated directions.

Informally, a finite domain is a finite set of arbitrary elements.

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, a superkey is a set of attributes within a table whose values can be used to uniquely identify a tuple.

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, it is the similarity between observations as a function of the time separation between them.

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

Informally, a Lyapunov function is a function that takes positive values everywhere except at the equilibrium in question, and decreases ( or is non-increasing ) along every trajectory of the ODE.

Informally, it reflects the difficulty inherent in approximating a discontinuous function by a finite series of continuous sine and cosine waves.

Informally, the identity asserts that the sum of the squares of the Fourier coefficients of a function is equal to the integral of the square of the function,

Informally, and using programming language jargon, a tree ( xy ) can be thought of as a " function " x applied to an

Informally, a computational problem consists of problem instances and solutions to these problem instances.

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 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 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 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 word is also used to describe a procedure or process with a specific purpose.

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, the term measure word is also sometimes used to refer to numeral classifiers, which are used with nouns that are countable in some languages.

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 algorithm constructs a finite state machine that resembles a trie with additional links between the various internal nodes.

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, in the tradition of the Afro-Brazilian syncretic religion Umbanda, Sebastian is often associated with Oxossi, especially in the state of Rio de Janeiro itself.

Informally, free abelian groups or formal sums may also be seen as signed multisets with elements in B.

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, 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, 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 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, 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, flak jacket may refer to a ballistic vest, particularly Type III and above, which is reinforced with either steel, titanium, ceramic, or polyethylene plates.

Informally, there are city areas with colloquial labels.

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, 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.