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

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, 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, 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 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, 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.

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 name often used for the entire West Coast Region, of which the Westland District is a part

Informally, the name " NFL Europe " continued to be used in the United States, including for the league's English-language Web site, nfleurope. com.

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, however, scientists may still take advantage of the pathetic fallacy for quick and convenient metaphoric explanations of complex scientific concepts in a readily understood way.

Informally this has been called the " Step Boundary ", although the step-like shape of the boundary was not apparent for several decades — the source of the Arkansas, believed to be near the 42nd parallel, was not known until John C. Frémont located it in the 1840s, hundreds of miles south of the 42nd parallel.

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

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, a path expression is a sequence of steps separated by the "" operator, for example ( which is short for ).

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, the gold fixing provides a recognized rate that is used as a benchmark for pricing the majority of gold products and derivatives throughout the world's markets.

Informally the portion of the Torah read by or to the maftir is called the " maftir portion ", or the " maftir " for short: in a Chumash the word " maftir " is printed in the margin at the beginning of that portion.

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, the term " graph invariant " is used for properties expressed quantitatively, while " property " usually refers to descriptive characterizations of graphs.

Informally, a strategy for a player is a way of playing in which his plays are entirely determined by the foregoing plays.

Informally this deal was arranged personally by Demetris Christofias, president of Cyprus and most of the money for the contract was sponsored by Laiki Bank.

** Informally, any GPS navigation device, especially an automotive navigation system

Informally, reification is often referred to as " making something a first-class citizen " within the scope of a particular system.

Informally, the terms C standard library or C library or libc are also used to designate a particular implementation on a given system.

Informally, two crystals tend to be in the same crystal system if they have similar symmetries, though there are many exceptions to this.

Informally, an Hamiltonian system is a mathematical formalism to describe the evolution equations of a physical system.

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.

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 tangent bundle of a manifold ( in this case a circle ) is obtained by considering all the tangent spaces ( top ), and joining them together in a smooth and non-overlapping manner ( bottom ).

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, 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: a formula in prenex form containing existential quantifiers only is provable ( valid ) in first-order logic if and only if a disjunction composed of substitution instances of the quantifier-free subformula of is a tautology ( propositionally derivable ).