If numerical iterative methods have to be employed, the aim is to iterate until full machine accuracy is obtained ( the best that is possible with a finite word length on the computer, and within the mathematical and / or physical approximations made ).

In this way, Ω < sub > F </ sub > represents the probability that a randomly selected infinite sequence of 0s and 1s begins with a bit string ( of some finite length ) that is in the domain of F. It is for this reason that Ω < sub > F </ sub > is called a halting probability.

* It can also provide uniformly spaced samples of the continuous DTFT of a finite length sequence.

An important simplification occurs when the sequences are of finite length, N. In terms of the DFT and inverse DFT, it can be written as follows:

Modern school textbooks often define separate figures called lines ( infinite ), rays ( semi-infinite ), and line segments ( of finite length ).

The coupling of this corollary with the initial statement of the law proves every threaded discussion to be finite in length.

Rays from an object at finite distance are associated with a virtual image that is closer to the lens than the focal length, and on the same side of the lens as the object.

In mathematics, a polynomial is an expression of finite length constructed from variables ( also called indeterminates ) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

While billing is sometimes done using a flat per-game rate ( when the length of the game is known and finite ), games more typically use a per-turn cost schedule.

Equivalently, a module M is simple if and only if every cyclic submodule generated by a non-zero element of M equals M. Simple modules form building blocks for the modules of finite length, and they are analogous to the simple groups in group theory.

One particularly useful condition is that the length of the sequence is finite and each quotient module M < sub > i </ sub >/ M < sub > i + 1 </ sub > is simple.

For example, the Fitting lemma shows that the endomorphism ring of a finite length indecomposable module is a local ring, so that the strong Krull-Schmidt theorem holds and the category of finite length modules is a Krull-Schmidt category.

The Grothendieck group ignores the order in a composition series and views every finite length module as a formal sum of simple modules.

The geometric progression tells us that infinite stages could ideally fit into a finite axial length.

The finite length in this case is the full height of the housing as the bearings, the motor, and controller and some of the coolers can be installed inside on the axis.

Instead, some type of approximation of the sinc functions, finite in length, has to be used.

For a given prime and positive integers and with, a primitive narrow-sense BCH code over the finite field with code length and minimum distance at least is constructed by the following method.

A transmission line of finite length ( lossless or lossy ) that is terminated at one end with a resistor equal to the characteristic impedance appears to the source like an infinitely long transmission line.

However long a randomly generated finite string is, there is a small but nonzero chance that it will turn out to consist of the same character repeated throughout ; this chance approaches zero as the string's length approaches infinity.

For finite random sequences, Kolmogorov defined the " randomness " as the entropy, i. e. Kolmogorov complexity, of a string of length K of zeros and ones as the closeness of its entropy to K, i. e. if the complexity of the string is close to K it is very random and if the complexity is far below K, it is not so random.

As part of the development of Lebesgue integration, Lebesgue invented the concept of measure, which extends the idea of length from intervals to a very large class of sets, called measurable sets ( so, more precisely, simple functions are functions that take a finite number of values, and each value is taken on a measurable set ).

For example, in assigning a measure to R that agrees with the usual length of intervals, this measure must be larger than any finite real number.

Spread article on flat surface to required width before measuring length at center.

A variation, known as the great knout, consisted of a handle about long, to which was fastened a flat leather thong about twice the length of the handle, terminating with a large copper or brass ring to which was affixed a strip of hide about broad at the ring, and terminating at the end of in a point.

That chamber is constructed largely of flat slabs of stone, many of which traverse nearly the entire length of the walls.

Because of a property of compression within the tube, the length must be a little shorter to correct flat pitch.

The Po (,, ancient Ligurian: Bodincus or Bodencus, ) is a river that flows either or – considering the length of the Maira, a right bank tributary – eastward across northern Italy, from a spring seeping from a stony hillside at Pian del Re, a flat place at the head of the Val Po under the northwest face of Monviso ( in the Cottian Alps ) through a delta projecting into the Adriatic Sea near Venice.

Mathematical description of the surface area is considerably more involved than the definition of arc length or polyhedra ( objects with flat polygonal faces ) the surface area is the sum of the areas of its faces.

Reverse camber skis have tips and tails that curve up while the length between them is flat.

Though typically flat the whole length on heavy duty trucks, the rails may sometimes be tapered or arched for clearance around the engine or over the axles.

This metric has only two undetermined parameters: an overall length scale R that can vary with time, and a curvature index k that can be only 0, 1 or − 1, corresponding to flat Euclidean geometry, or spaces of positive or negative curvature.

Hero of Alexandria ( Heron ) ( c. 60 ) described a principle of reflection, which stated that a ray of light that goes from point A to point B, suffering any number of reflections on flat mirrors, in the same medium, has a smaller path length than any nearby path.

The British socket bayonet had a triangular blade with a flat side towards the muzzle and two fluted sides outermost to a length of 15 inches ( 38 cm ).

An intrinsic definition of the Gaussian curvature at a point P is the following: imagine an ant which is tied to P with a short thread of length r. She runs around P while the thread is completely stretched and measures the length C ( r ) of one complete trip around P. If the surface were flat, she would find C ( r ) = 2πr.

The principal advantage of the Zaschka machine is in its ability to remain motionless in the air for any length of time and to descend in a vertical line, so that a landing may be accomplished on the flat roof of a large house.

The coat is flat with light feathering of long length or short length depending on the type.

This vast flat, the modern El-Jezireh, is about in length, interrupted only by a single limestone range rising abruptly out of the plain, and branching off from the Zagros mountains under the names of Sarazur, Hainrin and Sinjar.

Near the center of this square is the pitcher's circle, and within the circle is the " rubber ", a small flat rectangular piece of rubber about a foot and a half in length.

a railway bridge made of steel, 2, 500m in length and 41m in height, was constructed in 1913 to take the Neumünster – Flensburg railway over the Kiel Canal from the relatively flat land on either side.

One way to picture this is to imagine a flat soap film bounded on one side by a taut thread of length, L. The thread will be pulled toward the interior of the film by a force equal to 2L ( the factor of 2 is because the soap film has two sides, hence two surfaces ).

In this case, for two events which are simultaneous according the cosmological time coordinate, the value of the cosmological proper distance is not equal to the value of the proper length between these same events ,( Wright ) which would just be the distance along a straight line between the events in a Minkowski diagram ( and a straight line is a geodesic in flat Minkowski spacetime ), or the coordinate distance between the events in the inertial frame where they are simultaneous.

This forces the metal to grow in length ( and width if left unchecked ) much faster than just hammering with the flat face of the hammer.

These blades had deep fullers running their length, yet still had single-handed hilts which sported a unique shaped pommel, flat at the grip side and roughly triangular early on, with the flat curving to fit the hand later.