Set-theoretically, one may represent a binary function as a subset of the Cartesian product X × Y × Z, where ( x, y, z ) belongs to the subset if and only if f ( x, y ) = z.

Intellectual production comes to be seen as a product of an individual, with attendant rights, rather than purely a collective or social product which belongs in the commons.

A TARDIS is a product of the advanced technology of the Time Lords, an extraterrestrial civilization to which the program's central character, the Doctor, belongs.

In terms of the underlying linear algebra, a point belongs to a line if the inner product of the vectors representing the point and line is zero.

Nowadays Hollister's wristband identification product line belongs to Precision Dynamics Corporation, as stated in Hollister's site.

Elizabeth A. Lerner, a Unitarian Universalist minister and the product of a mixed marriage, belongs to a religion that has traditionally not actively sought converts from other belief systems.

A choice function ( selector, selection ) is a mathematical function f that is defined on some collection X of nonempty sets and assigns to each set S in that collection some element f ( S ) of S. In other words, f is a choice function for X if and only if it belongs to the direct product of X.

Driven by consumer demand, the ethnic food market reached record sales in 2002, and has emerged as the fastest growing category in the food and beverage product sector, according to USBX Advisory Services.

" An abstraction " is the product of this process – a concept that acts as a super-categorical noun for all subordinate concepts, and connects any related concepts as a group, field, or category.

The interpretation of an n-ary morphism as an ordinary morphisms whose domain is some sort of product of the domains of the original n-ary morphism will work in a monoidal category.

These categories surely have some objects that are " special " in a certain way, such as the empty set or the product of two topologies, yet in the definition of a category, objects are considered to be atomic, i. e., we do not know whether an object A is a set, a topology, or any other abstract concept – hence, the challenge is to define special objects without referring to the internal structure of those objects.

In category theory, currying can be found in the universal property of an exponential object, which gives rise to the following adjunction in cartesian closed categories: There is a natural isomorphism between the morphisms from a binary product and the morphisms to an exponential object.

The difference is that the Cartesian product can be interpreted simply as a pair of items ( or a list ), whereas the tensor product, used to define a monoidal category, is suitable for describing entangled quantum states.

When they claim that their product is the " best ", they mean that the product is as good as the other superior products in its category.

More abstractly, one talks about the product in category theory, which formalizes these notions.

Formally, a bifunctor is a functor whose domain is a product category.

Tensor products: If C denotes the category of vector spaces over a fixed field, with linear maps as morphisms, then the tensor product defines a functor C × C → C which is covariant in both arguments.

Cisgenesis, sometimes also called Intragenesis, is a product designation for a category of genetically engineered plants.

* For the general treatment of the concept of a product, see product ( category theory ), which describes how to combine two objects of some kind to create an object, possibly of a different kind.

** the product category, a category that is the product of categories.

This shows that the product of rings is an instance of products in the sense of category theory.

However, despite also being called the direct sum of rings when I is finite, the product of rings is not a coproduct in the sense of category theory.

The product in this category is given by the cartesian product of sets.

Let X and Y be objects of a category D. The product of X and Y is an object X × Y together with two morphisms

To understand this characterization as a terminal property we take the category C to be the product category D × D and define the diagonal functor

Primitive catapults were essentially “ the product of relatively straightforward attempts to increase the range and penetrating power of missiles by strengthening the bow which propelled them ”.

Lutz goes on to say that when advertisers state that their product is “ good ", it is equivalent in meaning to saying that their product is the best.

A former senior product manager at Master Lock, a trigger lock manufacturer, was quoted as saying “ If you put a trigger lock on any loaded gun, you are making the gun more dangerous .” Critics also point out that a trigger lock will increase the time it takes a gun owner to respond to a self-defense emergency.

The finished product was built in admirable form for the Roman Emperor, “ All of these elements marvelously fitted together in mid-air, suspended from one another and reposing only on the parts adjacent to them, produce a unified and most remarkable harmony in the work, and yet do not allow the spectators to rest their gaze upon any one of them for a length of time .”

However, while pasta is made everywhere, “ the product from Italy keeps to time-tested production methods that create a superior pasta ”.

The end product of this effort is what the industry terms as-built drawings, or more simply, “ as built .” The requirement for providing them is a norm in construction contracts.

" This provision prevents the existence of two ‘ grades ’ of whisky originating from Scotland, one “ Scotch whisky ” and the other, a “ whisky – product of Scotland ” that complies with the generic EU standard for whisky.

Turgot was one of the first to recognize that “ successive applications of the variable input will cause the product to grow, first at an increasing rate, later at a diminishing rate until it reaches a maximum .” This was a recognition that the productivity gains required to increase national wealth had an ultimate limit, and, therefore, wealth was not infinite.

“ Product differentiation .” http :// economicswebinstitute. org / glossary / product. htm

What is considered “ functional ” depends upon the specific product or thing sought to be protected.

To gain registration in the Principal Register or common law protection under the Lanham Act, a trade dress must be “ distinctive .” This means that consumers perceive a particular trade dress as identifying a source of a product.

Claimed trade dress in the product design -- as opposed to product packaging -- context can no longer be “ inherently distinctive ”; it must acquire distinctiveness through “ secondary meaning .” Wal-Mart Stores, Inc. v. Samara Brothers, Inc., 529 U. S. 205, 120 S. Ct. 1339, 146 L. Ed.

" In a 1977 essay on Catch-22, Heller stated that the “ antiwar and antigovernment feelings in the book ” were a product of the Korean War and the 1950s rather than World War II itself.

In 1705, de Moivre discovered, intuitively, that “ the centripetal force of any planet is directly related to its distance from the centre of the forces and reciprocally related to the product of the diameter of the evolute and the cube of the perpendicular on the tangent ”.

There is often a “ product over process ” approach to science journalism that aids, too, in the downplaying of uncertainty.

Griffith was unsure of his final product and took several months to complete the editing saying “ I can ’ t look at the damn thing ; it depresses me so .”

According to the Mining Gazette of July 25, 1886, “ The materials used with the exception of the facing brick are the product of the Upper Peninsula ”( p. 3 ).

In rejecting bank sales of accounts that functioned like mutual funds, the Supreme Court explained in Investment Company Institute v. Camp that it would have given “ deference ” to the OCC ’ s judgment if the OCC had explained how such sales could avoid the conflicts of interest and other “ subtle hazards ” Glass-Steagall sought to prevent and that could arise when a bank offered a securities product to its customers.

President Bill Clinton ’ s signing statement for the GLBA summarized the established argument for repealing Glass-Steagall Section ’ s 20 and 32 in stating that this change, and the GLBA ’ s amendments to the Bank Holding Company Act, would “ enhance the stability of our financial services system ” by permitting financial firms to “ diversify their product offerings and thus their sources of revenue ” and make financial firms “ better equipped to compete in global financial markets .”