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In mathematics, a **product** is the result of multiplying, or an expression that identifies factors to be multiplied. Thus, for instance, 6 is the product of 2 and 3 (the result of multiplication), and is the product of and (indicating that the two factors should be multiplied together).

The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication. When matrices or members of various other associative algebras are multiplied, the product usually depends on the order of the factors. Matrix multiplication, for example, and multiplication in other algebras is in general non-commutative.

There are many different kinds of products in mathematics: besides being able to multiply just numbers, polynomials or matricies, one can also define products on many different algebraic structures. An overview of these different kinds of products is given here.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Product_(mathematics)

**Mathematics** (from Greek μάθημα *máthēma*, “knowledge, study, learning”) is the study of topics such as quantity (numbers),structure,space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.

Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's *Elements*. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Mathematics

**The Servant** was an English alternative band, formed in London in 1998. They are popular in France, Spain, Switzerland as well as other European countries.

Their first introduction to an American audience was in the trailer of the film *Sin City* with the instrumental version of their song "Cells". This version of "Cells" is not on the *Sin City* soundtrack, but it can be downloaded via their website ("Cells" was also used in the film *The Transporter and Transporter 2*, along with their song, "Body"). Since the *Sin City* trailers, there has been significant U.S. interest in their records and demands for live concerts. The band released their fourth album entitled *How To Destroy A Relationship* in 2006.

Before achieving commercial success in 2004 with their self-titled album, released by Prolifica Records in the UK and by Recall Group in France, The Servant released two EP's: *Mathematics* in 1999 and *With the Invisible* in 2000.

On 26 November 2007, the band announced on their blog at MySpace that they were splitting up "to move on to pastures new".

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/The_Servant_(band)

**Mathematics**, also known as **Allah Mathematics**, (born: **Ronald Maurice Bean**) is a hip hop producer and DJ for the Wu-Tang Clan and its solo and affiliate projects.

Born and raised in Jamaica, Queens, New York, Mathematics was introduced to hip hop by his brother who used to bring home recordings of the genre's pioneers like Grandmaster Flash & The Furious Five, Treacherous Three and Cold Crush Brothers. He began his career in 1987 DJing block parties and park jams in Baisley Projects, going by the name Supreme Cut Master. In 1988, he became the full-time DJ for experienced rapper Victor C, doing countless shows in clubs and colleges in New York City.

In 1990, Mathematics linked up with GZA/Genius; he soon became one of the Wu-Tang Clan's founding members, but at the time GZA was struggling to build a career on the Cold Chillin' label. This partnership earned Mathematics a spot on his first official tour, The Cold Chillin Blizzard Tour (with popular acts such as Biz Markie, Big Daddy Kane, Kool G. Rap & DJ Polo and Marley Marl).

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Mathematics_(producer)

**Product** may refer to:

In **linear algebra**:

- Dot product
- Cross product
- Seven-dimensional cross product
- Triple product in vector calculus

In **abstract algebra**:

- Direct product of groups
- Semidirect product
- Product of group subsets
- Wreath product
- Free product
- Zappa–Szép product (or knit product), a generalization of the direct and semidirect products

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Product

In project management, a **product breakdown structure** (PBS) is a tool for analysing, documenting and communicating the outcomes of a project, and forms part of the product based planning technique.

The PBS provides ''an exhaustive, hierarchical tree structure of deliverables (physical, functional or conceptual) that make up the project, arranged in whole-part relationship'' (Duncan, 2015).

This diagrammatic representation of project outputs provides a clear and unambiguous statement of what the project is to deliver.

The PBS is identical in format to the work breakdown structure (WBS), but is a separate entity and is used at a different step in the planning process. The PBS precedes the WBS and focuses on cataloguing all the desired outputs (products) needed to achieve the goal of the project. This feeds into creation of the WBS, which identifies the tasks and activities required to deliver those outputs. Supporters of product based planning suggest that this overcomes difficulties that arise from assumptions about what to do and how to do it by focusing instead on the goals and objectives of the project - an oft-quoted analogy is that PBS defines where you want to go, the WBS tells you how to get there.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Product_breakdown_structure

In category theory, the **product** of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct product of rings and the product of topological spaces. Essentially, the product of a family of objects is the "most general" object which admits a morphism to each of the given objects.

Let **C** be a category with some objects *X*_{1} and *X*_{2}. An object *X* is a product of *X*_{1} and *X*_{2}, denoted *X*_{1} × *X*_{2}, if it satisfies this universal property:

The unique morphism *f* is called the **product of morphisms** *f*_{1} and *f*_{2} and is denoted < *f*_{1}, *f*_{2} >. The morphisms *π*_{1} and *π*_{2} are called the **canonical projections** or **projection morphisms**.

Above we defined the **binary product**. Instead of two objects we can take an arbitrary family of objects indexed by some set *I*. Then we obtain the definition of a **product**.

An object *X* is the product of a family (*X*_{i})_{i∈I} of objects iff there exist morphisms *π*_{i} : *X* → *X*_{i}, such that for every object *Y* and a *I*-indexed family of morphisms *f*_{i} : *Y* → *X*_{i} there exists a unique morphism *f* : *Y* → *X* such that the following diagrams commute for all *i*∈*I*:

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Product_(category_theory)

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