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.

Informally, a graph is a good expander if it has low degree and high expansion parameters.

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

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 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, the market spilled into the surrounding neighborhood, both in terms of street vendors and in terms of the nearby Magazin Universal (" Universal Store ") named Bucur Obor, a large commercial building that has been parcelled up into hundreds of small, independent retail stores.

Informally, one might say that the Dirac string carries away the " excess curvature " that would otherwise prevent F from being a closed form, as one has that everywhere except at the location of the monopole.

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, this means that if G acts unitarily on a Hilbert space and has " almost invariant vectors ", then it has a nonzero invariant vector.

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, a topological property is a property of the space that can be expressed using open sets.

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

Informally, we can consider these products on the left hand side as being elements of the free group F =

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, 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, 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 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, the function type refers to the set of functions that, given an input of type, produce an output of type.

Informally, the lemma immediately gives a precise sense in which finitely generated modules over a commutative ring behave like vector spaces over a field.

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

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 relational database table is often described as " normalized " if it is in the Third Normal Form.

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, this means that arguments of this form do not give good reason to establish their conclusions, even if their premises are true.

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.