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

Informally speaking, continuations can account for the similarity between such sentences as " Alice sees Bob "— formally, — and " Alice sees everyone ", i. e..

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 " 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.

A pure or homogeneous simplicial k-complex is a simplicial complex where every simplex of dimension less than k is a face of some simplex of dimension exactly k. Informally, a pure 1-complex " looks " like it's made of a bunch of lines, a 2-complex " looks " like it's made of a bunch of triangles, etc.

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, two sets are close in the Hausdorff distance if every point of either set is close to some point of the other set.

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 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.

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, C can be regarded as the *- algebra of continuous complex-valued functions over the compact matrix quantum group, and u can be regarded as a finite-dimensional representation of the compact matrix quantum group.

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, 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 it solves the following problem: Given an integer N, find its prime factors.

Informally referred to as the M6 " Classic " to distinguish it from the " M6 TTL " models, and to indicate its " Classic " M3 dimensions.

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, the Parliament is involved by the Commission since the beginning of the procedure, in order to guarantee its consent, although the Treaties do not formally forecast it.

Informally referred to as the M6 " Classic " to distinguish it from the " M6 TTL " models, and to indicate its " Classic " M3 dimensions.

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

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 computational problem consists of problem instances and solutions to these problem instances.

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, input positions can be thought of as locations at token boundaries.

* Informally known as FORTRAN 66.

* Informally known as Fortran 90.

* Informally known as Fortran 95.

* Informally known as Fortran 2003.

* Informally known as Fortran 2008.

Informally, the expression " infinitesimal calculus " became commonly used to refer to Weierstrass ' approach but has become something of a dead metaphor.

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.