Hamming space

In statistics and coding theory, a Hamming space is usually the set of all binary strings of length N. It is used in the theory of coding signals and transmission.

More generally, a Hamming space can be defined over any alphabet (set) Q as the set of words of a fixed length N with letters from Q. If Q is a finite field, then a Hamming space over Q is an N-dimensional vector space over Q. In the typical, binary case, the field is thus GF(2) (also denoted by Z₂).

In coding theory, if Q has q elements, then any subset C (usually assumed of cardinality at least two) of the N-dimensional Hamming space over Q is called a q-ary code of length N; the elements of C are called codewords. In the case where C is a linear subspace of its Hamming space, it is called a linear code. A typical example of linear code is the Hamming code. Codes defined via a Hamming space necessarily have the same length for every codeword, so they are called block codes when it is necessary to distinguish them from variable-length codes that are defined by unique factorization on a monoid.

Code (album)

Code (stylized as C O D E) is an album by British electronic band Cabaret Voltaire. The track "Don't Argue" was released as a single, as was "Here To Go".

The lyrics (and title) of "Don't Argue" incorporate verbatim a number of sentences from the narration of the 1945 short film Your Job in Germany, directed by Frank Capra. The film was aimed at American soldiers occupying Germany and strongly warned against trusting or fraternizing with German citizens.

Track listing

Personnel

Code (law)

A code is a type of legislation that purports to exhaustively cover a complete system of laws or a particular area of law as it existed at the time the code was enacted, by a process of codification. Though the process and motivations for codification are similar in different common law and civil law systems, their usage is different. In a civil law country, a Code typically exhaustively covers the complete system of law, such as civil law or criminal law. By contrast, in a common law country with legislative practices in the English tradition, a Code is a less common form of legislation, which differs from usual legislation that, when enacted, modify the existing common law only to the extent of its express or implicit provision, but otherwise leaves the common law intact. By contrast, a code entirely replaces the common law in a particular area, leaving the common law inoperative unless and until the code is repealed. In a third case of slightly different usage, in the United States and other common law countries that have adopted similar legislative practices, a Code is a standing body of statute law on a particular area, which is added to, subtracted from, or otherwise modified by individual legislative enactments.

Mathematical object

A mathematical object is an abstract object arising in mathematics. The concept is studied in philosophy of mathematics.

In mathematical practice, an object is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs. Commonly encountered mathematical objects include numbers, permutations, partitions, matrices, sets, functions, and relations. Geometry as a branch of mathematics has such objects as hexagons, points, lines, triangles, circles, spheres, polyhedra, topological spaces and manifolds. Another branch—algebra—has groups, rings, fields, group-theoretic lattices, and order-theoretic lattices. Categories are simultaneously homes to mathematical objects and mathematical objects in their own right. In proof theory, proofs and theorems are also mathematical objects.

The ontological status of mathematical objects has been the subject of much investigation and debate by philosophers of mathematics.

Cantorian framework

Three Imaginary Boys

Three Imaginary Boys is the debut studio album by English rock band the Cure, who were at that time a trio. It was released on 8 May 1979 by record label Fiction. It was later released in the United States and Australia with a different song tracklist as Boys Don't Cry.

Background

The record company decided which songs were put on the album, as well as the cover artwork, without Robert Smith's consent. For all Cure albums since, Smith has ensured he is given complete creative control over the final product before it goes on sale.

The "Foxy Lady" soundcheck, with vocals sung by Michael Dempsey, was not supposed to be on the album, and was removed for the American release. Smith has stated that "songs like 'Object' and 'World War' and our cover of 'Foxy Lady' were [Chris Parry's] choice".

Release

Three Imaginary Boys was released on 8 May 1979 by record label Fiction.

The album was reissued on 29 November 2004 and featured a second disc of unreleased material, including songs recorded under the band name "Easy Cure" with Porl Thompson. It was originally supposed to be released in early 2004 along with the band's next three studio albums (Seventeen Seconds, Faith and Pornography), but was delayed multiple times before being released by itself at the end of 2004. Since it featured a variety of old songs, it was the only Deluxe Edition by the band which did not include an alternate version of each song on the first disc. Some of the early booklets in the reissue had missing lyrics, which were made available on the Cure's website in PDF form. All copies since contain the lyrics.

Goal

A goal is a desired result that a person or a system envisions, plans and commits to achieve: a personal or organizational desired end-point in some sort of assumed development. Many people endeavor to reach goals within a finite time by setting deadlines.

It is roughly similar to purpose or aim, the anticipated result which guides reaction, or an end, which is an object, either a physical object or an abstract object, that has intrinsic value.

Goal setting

Goal setting may involve establishing specific, measurable, achievable, relevant, and time-bounded (SMART) objectives, but not all researchers agree that these SMART criteria are necessary.

Research on goal setting by Edwin A. Locke and his colleagues suggests that goal setting can serve as an effective tool for making progress when it ensures that group members have a clear awareness of what each person must do to achieve a shared objective. On a personal level, the process of setting goals allows individuals to specify and then work toward their own objectives (such as financial or career-based goals). Goal-setting comprises a major component of personal development and management.