In mathematics, a Cauchy sequence ( pronounced ), named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.

The shoot-out that ends Sergio Leone's Spaghetti Western " Dollars " trilogy is a notable example of how these elements work together to produce an effect: The shot selection goes from very wide to very close and tense ; the length of shots decreases as the sequence progresses towards its end ; the music builds.

The sequence progresses from the planet's formation to the first living creatures, followed by the reign and extinction of the dinosaurs.

As the game progresses, each player in turn must recite one to three numbers, counting in sequence from where the previous player left off:

The male's narrative begins at the beginning of the story and progresses through marriage, infidelity, and divorce, while the female narrative begins at the end of the relationship and ends with the couple's first date ; the two actors ' only direct interaction takes place midpoint, during the wedding sequence.

Server-side game code makes a trade-off between calculating and sending results for display on a just-in-time basis or trusting the client to calculate and display the results in appropriate sequence as a player progresses.

As the japa progresses the Nadi's are cleared in a certain sequence leading to a healthy body and mind.

Setting up a sequence of cameras to photograph the movement of a subject as it progresses in locomotion originally created chronophotographs.

Each level is loaded separately, in sequence as the game progresses.

Although astronomers agree that the diagram shows the sequence in which stars evolve, they argue about which way the sequence progresses.

The video progresses into a sequence of dreams, containing varied surrealistic, mystic, new age, sufi and Egyptian imagery and symbolism.

The dream sequence progresses with surreal and unusual clips, including Madonna in a pool with half-shown skulls.

While each scene has its own character and completeness it must fit into the general sequence to which it belongs.

DNA sequence analysis indicated that Liliales should be divided into at least Liliales, Asparagales and Dioscoreales.

On systems with 32-bit or larger words, it is possible to speed up execution of this cipher by combining the < tt > SubBytes </ tt > and < tt > ShiftRows </ tt > steps with the < tt > MixColumns </ tt > step by transforming them into a sequence of table lookups.

When 301 of the most advanced model, the " Launch Arco ," are built, an " exodus sequence " starts in which all Launch Arcos blast into space.

Upon heating, α-berkelium transforms into another phase with an fcc lattice ( but slightly different from β-berkelium ), space group Fmm and the lattice constant of 500 pm ; this fcc structure is equivalent to the closest packing with the sequence ABC.

For example, methods to locate a gene within a sequence, predict protein structure and / or function, and cluster protein sequences into families of related sequences.

Beechcraft was not Beech's first company, as he had previously formed Travel Air in 1924 and the design numbers used at Beechcraft followed the sequence started at Travel Air, and were then continued at Curtiss-Wright, after Travel Air had been absorbed into the much larger company in 1929.

Using the extension of the code, the encoded string 0011001011 can be grouped into codewords as 0 – 011 – 0 – 01 – 011, and these in turn can be decoded to the sequence of source symbols acabc.

A code is a total function mapping each symbol from S to a sequence of symbols over T, and the extension of M to a homomorphism of into, which naturally maps each sequence of source symbols to a sequence of target symbols, is referred to as its extension.

Bolzano's proof relied on the method of bisection: the sequence was placed into an interval that was then divided into two equal parts, and a part containing infinitely many terms of the sequence was selected.

* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then

The mRNA code is then translated into an amino acid chain ( sequence ) that comprises the newly made protein.

When scientists transfer a gene from one cell into another cell in order to express the new genetic material as a protein in the recipient cell, the cDNA will be added to the recipient ( rather than the entire gene ), because the DNA for an entire gene may include DNA that does not code for the protein or that interrupts the coding sequence of the protein ( e. g., introns ).

The goal of the company was to sequence the entire human genome and release it into the public domain for non-commercial use in much less time and for much less cost than the public human genome project.

The clip is incorporated into the series ' opening credit sequence from the third season onward.

The sequence of N complex numbers x < sub > 0 </ sub >, ..., x < sub > N − 1 </ sub > is transformed into another sequence of N complex numbers according to the DFT formula:

Division of labour is a process whereby the production process is broken down into a sequence of stages and workers are assigned to particular stages.

One of the basic tenets of Euclidean geometry is that two figures ( that is, subsets ) of the plane should be considered equivalent ( congruent ) if one can be transformed into the other by some sequence of translations, rotations and reflections.

An exon is a sequence of DNA that is expressed ( transcribed ) into RNA and then translated into protein.

For 2-dimensional tilings, they can be given by a vertex configuration listing the sequence of faces around every vertex.

This polyhedron is a part of a sequence of rhombic polyhedra and tilings with Coxeter group symmetry.

The triakis tetrahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane.

The triakis octahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane.

The triakis icosahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane.

This polyhedron is topologically related as a part of sequence of polyhedra and tilings of pentagons with face configurations ( V3. 3. 3. 3. n ).

to this he glued and fitted other pieces of paper and four taut strings, thus creating a sequence of flat surfaces in real and sculptural space to which there clung only the vestige of a picture plane.

On the one hand, Bernard Bolzano ( 1817 ) had been aware that any bounded sequence of points ( in the line or plane, for instance ) has a subsequence that must eventually get arbitrarily close to some other point, called a limit point.

In particular, the limit is taken as the complex number z approaches z < sub > 0 </ sub >, and must have the same value for any sequence of complex values for z that approach z < sub > 0 </ sub > on the complex plane.

A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments ( i. e., by a closed polygonal chain ).

Cabo de Gata-Níjar Natural Park was used for the road, tunnel and beach sequence in which birds strike the plane.

He rode in a biplane to record the sounds for the dogfight sequence, and visited the demolition of a wind turbine for the plane crashes.

Boy's ( the case p = 3 ) and Morin's ( the case p = 2 ) surfaces are beginning of a sequence of half-way models with higher symmetry first proposed by George Francis, indexed by the even integers 2p ( for p odd, these immersions can be factor through a projective plane ).

When American Airlines Flight 11 flew by overhead, Jules turned the camera to follow the plane and taped one of only three known recordings of the first plane hitting the North Tower ( Tower 1 ) of the World Trade Center, the others being a video shot by Pavel Hlava and a sequence of still frames taken by Wolfgang Staehle.

Lin's plane was travelling away from the Soviet Union at the time of its crash, making the exact sequence of events before Lin's death more confusing, and casting doubt on the possibility that Lin was attempting to seek asylum in the USSR.

One of the original ideas for the film's ending included a sequence with Scorpio kidnapping a group of schoolchildren at an airport, then attempting to hijack a plane.

After September 11, 2001, an email was circulated claiming that entering ' Q33 NY ', which it claims is the flight number of the first plane to hit the Twin Towers, in Wingdings would bring up a character sequence of a plane flying into two towers, followed by the skull and crossbones symbol and the Star of David.

In archaeology a section is a view in part of the archaeological sequence showing it in the vertical plane, as a cross section, and thereby illustrating its profile and stratigraphy.

This means the following: take a point ( α, β ) in the plane, and then consider the sequence of points

As with plane triangles, on a sphere two triangles sharing the same sequence of angle, side, angle ( ASA ) are necessarily congruent ( that is, they have three identical sides and three identical angles ).

Sierpiński curves are a recursively defined sequence of continuous closed plane fractal curves discovered by Wacław Sierpiński, which in the limit completely fill the unit square: thus their limit curve, also called the Sierpiński curve, is an example of a space-filling curve.

It is known that any non-singular rational variety is obtained from the plane by a sequence of blowing up transformations and their inverses (' blowing down ') of curves, which must be of a very particular type.

Motion estimation techniques can determine that on a two dimensional plane the ball is moving up and to the right and vectors describing this motion can be extracted from the sequence of frames.

It has a take-off sequence consisting of the plane lifting off the ground and leveling off, then a fade-out and the film resumes with a shot of the plane in the skies and the scene with Anne Redding and Paul Whitley meeting on board the jet.