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 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, 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, the Levenshtein distance between two words is equal to the number of single-character edits required to change one word into the other.

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 the name also refers to a larger district, the Monte Carlo Quarter ( corresponding to the former municipality of Monte Carlo ), which besides Monte Carlo / Spélagues also includes the wards of La Rousse / Saint Roman, Larvotto / Bas Moulins, and Saint Michel.

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

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

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 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, 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, 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, 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.

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.

For a non-negative integer k, the kth Betti number b < sub > k </ sub >( X ) of the space X is defined as the rank of the abelian group H < sub > k </ sub >( X ), the kth homology group of X. Equivalently, one can define it as the vector space dimension of H < sub > k </ sub >( X ; Q ), since the homology group in this case is a vector space over Q.

More generally, given a field F one can define b < sub > k </ sub >( X, F ), the kth Betti number with coefficients in F, as the vector space dimension of H < sub > k </ sub >( X, F ).

It was stated in terms of Betti numbers: The kth and ( n − k ) th Betti numbers of a closed ( i. e. compact and without boundary ) orientable n-manifold are equal.

Denoting the number of rows of pins in a bean machine by n, the number of paths to the kth bin on the bottom is given by the binomial coefficient.

In particular, degrees of nodes ( here degree means the number of children ) are kept quite low: every node has degree at most O ( log n ) and the size of a subtree rooted in a node of degree k is at least F < sub > k + 2 </ sub >, where F < sub > k </ sub > is the kth Fibonacci number.

Here we show that the size of the ( sub ) tree rooted at any node x of degree d in the heap must have size at least F < sub > d + 2 </ sub >, where F < sub > k </ sub > is the kth Fibonacci number.

where is the kth Bernoulli number and is the Riemann zeta function.

Write N < sub > k </ sub > for the kth square triangular number, and write s < sub > k </ sub > and t < sub > k </ sub > for the sides of the corresponding square and triangle, so that

where p < sub > k </ sub > is the kth prime number.

: where H < sub > k </ sub > is the kth harmonic number.

In computer science, a selection algorithm is an algorithm for finding the kth smallest number in a list ( such a number is called the kth order statistic ).

where C is the total number of configurations, is the abundance of the ith ranked species in the kth configuration, and is the dominance-diversity probability.

In mathematics, the generalized taxicab number Taxicab ( k, j, n ) is the smallest number which can be expressed as the sum of j kth positive powers in n different ways.

For example, one could compute twice the number of generations forward for a node at the ( k + 1 )- th level compared to one at the kth.

The number of nodes in the kth shell is given by

The Heesch number of a figure S is the maximum value k such that there exists a tiling of the plane, and tile t within that tiling, for which that all tiles in the zeroth through kth coronas of t are congruent to S. In some work on this problem this definition is modified to additionally require that the union of the zeroth through kth coronas of t is a simply connected region.