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Product

Definition: Product

Product

Noun

1. Commodities offered for sale; "good business depends on having good merchandise"; "that store offers a variety of products".

2. The amount of an artifact that has been created by someone or some process; "they improve their product every year"; "they export most of their agricultural production".

3. A consequence of someone's efforts or of a particular set of circumstances; "skill is the product of hours of practice"; "his reaction was the product of hunger and fatigue".

4. A chemical substance formed as a result of a chemical reaction; "a product of lime and nitric acid".

5. A quantity obtained by multiplication; "the product of 2 and 3 is 6".

6. The set of elements common to two or more sets; "the set of red hats is the intersection of the set of hats and the set of red things".

Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved.

Date "product" was first used in popular English literature: sometime before 1588. (references)

Specialty Definition: Product

Domain	Definition
Computing	Product See tuple. Source: The Free On-line Dictionary of Computing.
Business	Transportable goods, non-transportable goods and services. Source: European Union. (references)
Economics	Any product intended for consumers or likely to be used by consumers, supplied whether for consideration or not in the course of a commercial activity and whether new, used or reconditioned. Source: European Union. (references)
Medicine	The active ingredient or combination of active ingredients of a medicinal product. Source: European Union. (references)
Mining	Percent of metal in ore. (references)
Source: compiled by the editor from various references; see credits.

Specialty Definition: Matrix multiplication

(From Wikipedia, the free Encyclopedia)

This article gives an overview of the various ways to multiply matrices.
The Einstein summation convention is used throughout.
Ordinary matrix product
By far the most important way to multiply matrices is the usual matrix multiplication. It is defined between two matrices only if the number of columns of the first matrix is the same as the number of rows of the second matrix. If A is an m-by-n matrix and B is an n-by-p matrix, then their product AB is an m-by-p matrix given by

(AB)_ij = A_irB_rj = a_i1 * b_1j + a_i2 * b_2j + ... + a_in * b_nj

for each pair i and j.
The following picture shows how to calculate the (AB)₁₂ element of AB if A is a 2x4 matrix, and B is a 4x3 matrix. Elements from each matrix are paired off in the direction of the arrows; each pair is multiplied and the products are added. The location of the resulting number in AB corresponds to the row and column that were considered.

Example

This notion of multiplication is important because A and B are interpreted as linear transformations (which is almost universally done), then the matrix product AB corresponds to the composition of the two linear transformations, with B being applied first. In general, matrix multiplication is not commutative; that is, AB is not equal to BA.
The complexity of matrix multiplication, if carried out naively, is O(n³), but more efficient algorithms do exist. Strassen's method, devised by Volker Strassen in 1969 and often referred to as "fast matrix multiplication", uses a mapping of bilinear combinations to reduce complexity to O(n^log₂(7)) (approximately O(n^2.807...)). In practice, though, it is rarely used since it is awkward to implement, lacking numerical stability. The constant factor involved is about 4.695 asymptotically; Winograd's method improves on this slightly by reducing it to an asymptotic 4.537.
The best algorithm currently known, which was presented by Don Coppersmith and S. Winograd in 1990, has an asymptotic complexity of O(n^2.376). It has been shown that the leading exponent must be at least 2.
Hadamard product
For two matrices of the same dimensions, we have the Hadamard product or entrywise product. The Hadamard product of two m-by-n matrices A and B, denoted by A · B, is an m-by-n matrix given by (A·B)[i,j]=A[i,j] * B[i,j]. For instance

Note that the Hadamard product is a submatrix of the Kronecker product (see below). Hadamard product is studied by matrix theorists, but it is virtually untouched by linear algebraists.

Kronecker product
For any two arbitrary matrices A=(a_ij) and B, we have the direct product or Kronecker product A B defined as

(the HTML entity ⊗ (&otimes;) represents the direct product, but is not supported on older browsers)
Note that if A is m-by-n and B is p-by-r then A B is an mp-by-nr matrix. Again this multiplication is not commutative.
For example
.

If A and B represent linear transformations V₁ → W₁ and V₂ → W₂, respectively, then A B represents the tensor product of the two maps, V₁ V₂ → W₁ W₂.

Common properties
All three notions of matrix multiplication are associative

A * (B * C) = (A * B) * C
and distributive:
A * (B + C) = A * B + A * C
and
(A + B) * C = A * C + B * C
and compatible with scalar multiplication:
c(A * B) = (cA) * B = A * (cB)

Scalar multiplication
The scalar multiplication of a matrix A=(a_ij) and a scalar r gives the product
rA=(r a_ij).

If we are concerns with matrices over a ring, then the above multiplicaion is sometimes called the left multiplication while the right multiplication is defined to be
Ar=(a_ij r).

When the underlying ring is commutative, for example, the real or complex number field, the two multiplications are the same. However, if the ring is not commutative, such as the quaternions, they may be different. For example

External links

WIMS Online Matrix Multiplier
MathWorld: Strassen's Formula

References

Strassen, Volker, Gaussian Elimination is not Optimal, Numer. Math. 13, p. 354-356, 1969
Coppersmith, D., Winograd S., Matrix multiplication via arithmetic progressions, J. Symbolic Comput. 9, p. 251-280, 1990
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Matrix multiplication."

Multiplication

(From Wikipedia, the free Encyclopedia)

Multiplication is a quick way of adding identical numbers. The result of multiplying numbers is called a product. The numbers being multiplied are called coefficients or factors, and individually as the multiplicand and multiplicator.

Notation
Multiplication can be denoted several different ways, and for all real numbers the different notations are equivalent. All of the following mean, "5 times 2":

The asterisk is often used on computers because it is a symbol on every keyboard, but it is never used when writing math by hand, and should only be used when there are no other alternatives. (This usage originated in the FORTRAN programming language). Frequently, multiplication is implied rather than specifically noted. This arises in Algebra and looks like:

5x
xy
This should only be done with variables that have one letter; with variable that have multiple letters (it is possible, and often less confusing, to write out the name of a variable rather than using a single letter, i.e. using "mass" instead of "m") it can become confusing as to where one variable ends and the other begins. It is also confusing to use this notation with just numbers because 52 could then mean fifty-two or five times two.
If the terms are not written out individually, then the product may be written with an ellipsis to mark out the missing terms. Thus, the product of all the natural numbers from 1 to 100 is 1 · 2 · ... · 99 · 100.
Alternatively, the product can be with the product symbol, which is a capital Pi from the Greek alphabet. This is defined as:

The subscript gives the symbol for a dummy variable (i in our case) and its lower value (m); the superscript gives its upper value. So for example:

One may also consider products of infinitely many terms; these are called infinite products. Notationally, we would replace n above by the infinity symbol (∞). The product of such a series is defined as the limit of the product of the first n terms, as n grows without bound. That is:

One can similarly replace m with negative infinity, and

for some integer m, provided both limits exist.

Definition
As for what multiplication means, the product of two whole numbers n and m is:

This is just a shorthand for saying, "Add m to itself n times." Expanding the above to make its meaning more clear:

m×n = m + m + m +...+ m

such that there are n m's added together. So for instance:

5×2 = 5 + 5 = 10
2×5 = 2 + 2 + 2 + 2 + 2 = 10
4×3 = 4 + 4 + 4 = 12
m×6 = m + m + m + m + m + m
Using this definition, it is easy to prove some interesting properties of multiplication. As the first two examples above hint at, the order in which to numbers are multiplied does not matter. This is called the commutative property and it turns out to be true in general that for any two numbers x and y:

x·y = y·x

Multiplication also has what is called the associative property. The associative property means that for any three numbers x, y, and z:

(x·y)z = x(y·z)

Note from algebra: the parentheses mean that the operations inside the parentheses must be done before anything outside the parentheses is done.
Multiplication is also has what is called a distributive property because:

x(y + z) = xy + xz

Also of interest is that any number times 1 is equal to itself, thus:

1·x = x

and this is called the identity property
What about zero? The initial definition above is little help because 1 is greater than zero. It is actually easier to define multiplication by zero using the second definition. So:

m·0 = m + m + m +...+ m

where there are zero m's added together. The sum of zero m's is zero, so

m·0 = 0

no matter what m is (as long as it is finite).
Multiplication with negative numbers also requires a little thought. First consider negative 1. For any positive integer m:

(-1)m = (-1) + (-1) +...+ (-1) = -m

This is an interesting fact that shows that any negative number is just negative one multiplied by a positive number. So multiplication with any integers can be represented by multiplication of whole numbers and (-1)'s. All that remains is to explicitly define (-1)(-1):

(-1)(-1) = -(-1) = 1

In this way, the multiplication of any two integers is defined. The definitions can be extended to larger and larger sets of numbers: first to fractions called the rational numbers, then to infinitely long decimals called real numbers, and then to the complex numbers.
Students are sometimes mystified when told that the result of multiplying no numbers is 1.
A formal recursive definition of multiplication can be given by the rules:

x.0 = 0
x.y = x + x.(y-1)

where x is an arbitrary quantity, and y is a natural number. Once multiplication has been defined for natural numbers, it can be extended to include integers, and then to real and complex numbers.

Computation
For fast ways to compute products of large numbers, see multiplication algorithms.
To multiply numbers using pencil and paper, you need to have a multiplication table (either in your head or on paper). You also need to know a "multiplication algorithm" (a way to multiply numbers) such as lattice multiplication.
See also:
Peasant multiplication
reciprocal

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Multiplication."

Product

(From Wikipedia, the free Encyclopedia)

There is more than one usage of the word product.
You will find them at:
Product (mathematics)
Product (business)

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Product."

Product (business)

(From Wikipedia, the free Encyclopedia)

In marketing, a product is anything that can be offered to a market that might satisfy a want or need. However it is much more than just a physical object. It is the complete bundle of benefits or satisfactions that buyers perceive they will obtain if they purchase the product. It is the sum of all physical, psychological, symbolic, and service attributes.
A product is similar to a good. In economics, a good is a physical object that is available in the marketplace. This differentiates it from a service which is a non-material product.

Three Aspects
There are three aspects to any product or service:
1 Core Benefits
in-use benefits
psychological benefits (eg.: self-image enhancement, hope, status, self worth)
problem reduction benefits(eg.: safety, convience)
2 Tangible Product or Service
product attributes and features
quality
styling
packaging protection and label information
brand name
3 Augmented Product or Service
warranty
installation
delivery
credit availability
after-sale service and maintenance

Classifying Products
Product management involves developing strategies and tactics that will increase product demand (referred to as primary demand) over the product's life cycle.
One useful technique in understanding a product is the Aspinwall Classification System. It classifies and rates products based on five variables:
1) replacement rate - how frequently is the product repurchased
2) gross margin - how much profit is obtained from each product (average selling price less average unit cost)
3) buyer goal adjustment - how flexible are the buyers' purchasing habits in regards to this product
4) duration of product satisfaction - how long will the product produce benefits for the user
5) duration of buyer search search behaviour - how long will they shop for the product
Types of Products

There are several types of products:
consumer products - used by end users
industrial products - used in the production of other goods
convenience goods - purchased frequently and with minimal effort
impulse goods - purchase stimulated by immediate sensory cues
emergency goods - goods required immediately
shopping goods - some comparison with other goods
specialty goods - extensive comparisons with other goods and a lengthy information search
unsought goods - eg.: cemetery plots, insurance
perishable goods - goods that will deteriate quickly even without use
durable goods - goods that survive multiple use occations
non-durable goods - goods that are used up in one use occation
capital goods - installations, equipment, and buildings
parts and materials - goods that go into a finished product
supplies and services - goods that facilitate production
commodities - undifferentiated goods (eg.: wheat, gold, sugar)
by-products - a product that results from the manufacture of another product

See Also

product management
marketing
service
brand
whole product
brand management
Finding related topics

list of marketing topics
list of management topics
list of economics topics
list of finance topics
list of human resource management topics
list of accounting topics
list of information technology management topics
list of business law topics
list of production topics
list of business ethics, political economy, and philosophy of business topics
list of business theorists
list of economists
list of corporate leaders
list of companies
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Product (business)."

Product (category theory)

(From Wikipedia, the free Encyclopedia)

In category theory, one defines products to generalize constructions such as the cartesian product of sets, the product of groups, the 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.
Suppose C is a category, I is a set, and for each i in I, an object X_i in C is given. An object X, together with morphisms p_i : X → X_i for each i in I is called a product of the family (X_i) if, whenever Y is an object of C and q_i : Y → X_i are given morphisms, then there exists precisely one morphism r : Y → X such that q_i = p_ir.
The above definition is an example of a universal property; in fact, it is a special limit. Not every family (X_i) needs to have a product, but if it does, then the product is unique in a strong sense: if p_i : X → X_i and p'_i : X ' → X_i are two products of the family (X_i), then there exists a unique isomorphism r : X → X ' such that p'_ir = p_i for each i in I.
An empty product (i.e. I is the empty set) is the same as a terminal object in C.
If I is a set such that all products for families indexed with I exist, then it is possible to choose the products in a compatible fashion so that the product turns into a functor C^I → C. The product of the family (X_i) is then often denoted by ΠX_i, and the maps p_i are known as the natural projections. We have a natural isomorphism

(where Mor_C(U,V) denotes the set of all morphisms from U to V in C, the left product is the one in C and the right is the cartesian product of sets).
If I is a finite set, say I = {1,...,n}, then the product of objects X₁,...,X_n is often denoted by X₁×...×X_n. Suppose all finite products exist in C, product functors have been chosen as above, and 1 denotes the terminal object of C corresponding to the empty product. We then have natural isomorphisms

These properties are formally similar to those of a commutative monoid.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Product (category theory)."

Product (mathematics)

(From Wikipedia, the free Encyclopedia)

In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. 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; in other words, matrix multiplication, and the multiplications in those other algebras, are non-commutative.
Several products are considered in mathematics:
Products of the various classes of numbers
The dot product and cross product are forms of multiplication of vectorss.
The product of matrices; see matrix multiplication.
The pointwise product of two functions.
Products in rings and fields of many kinds.
It is often possible to form the product of two (or more) mathematical objects to form another object of the same kind, e.g.
the cartesian product of sets,
the product of groups,
the product of rings,
the product of topological spaces,
for the general treatment, see product (category theory).
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Product (mathematics)."

Product management

(From Wikipedia, the free Encyclopedia)

Product Management is one of the four areas of marketing. The other three parts of the marketing mix are pricing, promotion, and distribution. Product management deals with questions like:
What products to produce and sell
What new products to add
What existing products to discontinue
How long will it take for a product to penetrate the market
How many products to have in the product line
How to balance a product portfolio
Whether to use a product differentiation strategy
What is the best product positioning
What brand name to use
Whether to use individual branding or family branding
Whether to use product bundling or product lining
What logo to use
Product Life Cycle considerations
Obsolescence considerations

see also: product, marketing, marketing management, brand management
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Product management."

Product of groups

(From Wikipedia, the free Encyclopedia)

In mathematics, given a group G and two subgroups H and K of G, one can define the product of H and K, denoted by HK as the set of all elements of the form hk, for all h in H and k in K. In general HK is not a subgroup (hkh'k' is not of the form hk); it is a subgroup if and only if one among H and K is a normal subgroup of G. Indeed, if this is the case (assume K is normal), hkh'k' = hh' h' ^-1kh'k' , and h' ^-1kh is an element of K, so that hh' is in H and h' ^-1kh'k' is in K, as required. An analogous argument shows that (hk)^-1 is of the form h'k' .
Of particular interest are products enjoying further properties, the semidirect product and the direct product. They allow also to construct a product of two groups not given as subgroups of a fixed group.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Product of groups."

Product of rings

(From Wikipedia, the free Encyclopedia)

In abstract algebra, it is possible to combine several rings into one large product ring. This is done as follows: if I is some index set and R_i is a ring for every i in I, then the cartesian product Π_{i in I} R_i can be turned into a ring by defining the operations coordinatewise, i.e.
(a_i) + (b_i) = (a_i + b_i)
(a_i) · (b_i) = (a_i · b_i)

The product of finitely many rings R₁,...,R_k is also written as R₁ × R₂ × ... × R_k.

Examples
The most important example is the ring Z/nZ of integers modulo n. If n is written as a product of prime powers (see fundamental theorem of arithmetic):

where the p_i are distinct primes, then Z/nZ is naturally isomorphic to the product ring

This follows from the Chinese remainder theorem.

Properties
If R = Π_{i in I} R_i is a product of rings, then for every i in I we have a surjective ring homomorphism p_i : R -> R_i which projects the product on the i-th coordinate. The product R, together with the projections p_i, has the following universal property:

if S is any ring and f_i : S -> R_i is a ring homomorphism for every i in I, then there exists precisely one ring homomorphism f : S -> R such that p_i o f = f_i for every i in I.

This shows that the product of rings is an instance of products in the sense of category theory.
If A is a (left, right, two-sided) ideal in R, then there exist (left, right, two-sided) ideals A_i in R_i such that A = Π_{i in I} A_i. Conversely, every such product of ideals is an ideal in R. A is a prime ideal in R if and only if all but one of the A_i are equal to R_i and the remaining A_i is a prime ideal in R_i.
An element x in R is a unit if and only if all of its components are units, i.e. if and only if p_i(x) is a unit in R_i for every i in I. The group of units of R is the product of the groups of units of R_i.
A product of more than one non-zero rings always has zero divisors: if x is an element of the product all of whose coordinates are zero except p_i(x), and y is an element of the product with all coordinates zero except p_j(y) (with i ≠ j), then xy = 0 in the product ring.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Product of rings."

Product topology

(From Wikipedia, the free Encyclopedia)

In topology, the cartesian product of topological spaces is turned into a topological space in the following way. Let I be a (possibly infinite) index set and suppose X_i is a topological space for every i in I. Set X = Π X_i, the cartesian product of the sets X_i. For every i in I, we have a canonical projection p_i : X -> X_i. The product topology on X is defined to be the coarsest topology (i.e. the topology with the fewest open sets) which turns all the maps p_i into continuous maps.
Explicitly, the topology on X can be described as follows. A subset of X is open if and only if it is a union of (possibly infinitely many) intersections of finitely many sets of the form p_i^-1(O), where i in I and O is an open subset of X_i. This implies that, in general, not all products of open sets need to be open in X.
We can describe a basis for the product topology in a simple way using the bases of the constituting spaces X_i. Suppose that for each i in I we choose a set Y_i which is either the whole space X_i or a basis element in that space, and let B be the product of the Y_i. Then, as long as X_i = Y_i, that is, we choose the entire space, for all but finitely many i in I, B will be a basis element of the product space, and a complete basis is generated in this way. In particular, this means that a finite product of spaces X has a simple basis given by products of bases in the X_i.

Examples
If one starts with the standard topology on the real line R and defines a topology on the product of n copies of R in this fashion, one obtains the ordinary Euclidean topology on Rⁿ.
The Cantor set is homeomorphic to the product of countably many copies of the discrete space {0,1} and the space of irrational numbers is homeomorphic to the product of countably many copies of the natural numbers, where again each copy carries the discrete topology.

Properties
The product topology is also called the topology of pointwise convergence because of the following fact: a sequence (or net) in X converges if and only if all its projections to the spaces X_i converge. In particular, if one considers the space X = R^I of all real valued functions on I, convergence in the product topology is the same as pointwise convergence of functions.
An important theorem about the product topology is Tychonoff's theorem: any product of compact spaces is compact. This is easy for finite products, but the statement is (surprisingly) also true for infinite products, when the proof requires the axiom of choice in some form.
The product space X, together with the canonical projections, can be characterized by the following universal property: If Y is a topological space, and for every i in I, f_i : Y -> X_i is a continuous map, then there exists precisely one continuous map f : Y -> X such that p_i\ o f = f_i for all i in I. This shows that the product space is a product in the sense of category theory.
To check whether a given map f : Y -> X is continuous, one can use the following handy criterion: f is continuous if and only if p_i o f is continuous for all i in I. In other words, if we write f as a tuple of its components, f=(f_i)_{i in I}, then f is continuous if and only if each of the f_i is. Checking whether a map g : X -> Z is continuous is usually more difficult; one tries to use the fact that the p_i are continuous in some way.

Relation to other topological notions

Separation
Every product of T₀ spacess is T₀
Every product of T₁ spacess is T₁
Every product of Hausdorff spaces is Hausdorff
Every product of Regular spaces is Regular
Every product of Tychonoff spaces is Tychonoff
A product of normal spaces need not be normal
Compactness
Every product of compact spaces is compact (Tychonoff's theorem)
A product of locally compact spaces need not be locally compact
Connectedness
Every product of connected (resp. path-connected) spaces is connected (resp. path-connected)
Every product of hereditarily disconnected spaces is hereditarily disconnected.

Please add more results like these
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Product topology."

Abbreviations & Acronyms: Product

The following table is compiled from various sources, across various languages. When English abbreviations or acronyms come from a non-English source, this is noted.
Entry	Source	Expression	Field
PRC	English	Product reporting code	N/A
Source: compiled by the editor, based on several corpora (additional references).

Synonyms: Product

Synonyms: intersection (n), mathematical product (n), merchandise (n), production (n), wares (n). (additional references)

Synonyms within Context: Product

Context	Synonyms within Context (source: adapted from Roget's Thesaurus).
Acquisition	Profit, earnings, winnings, innings, pickings, net profit; avails; income; (receipt); proceeds, produce, product; outcome, output; return, fruit, crop, harvest; second crop, aftermath; benefit; (good).
Effect	Noun: effect, consequence; aftergrowth, aftercome; derivative, derivation; result; resultant, resultance; upshot, issue, denouement; end; development, outgrowth, fruit, crop, harvest, product, bud.
Increase	Noun: increase, augmentation, enlargement, extension; dilatation; (expansion); increment, accretion; accession; development, growth; aggrandizement, aggravation; rise; ascent; exaggeration exacerbation; spread; (dispersion); flood tide; gain, produce, product, profit.
Merchandise	Noun: merchandise, ware, commodity, effects, goods, article, stock, product, produce, staple commodity; stock in trade; (store); cargo; (contents).
Number	Sum, difference, complement, subtrahend; product; multiplicand, multiplier, multiplicator; coefficient, multiple; dividend, divisor, factor, quotient, submultiple; fraction, rational number; surd, irrational number; transcendental number; mixed number, complex number, complex conjugate; numerator, denominator; decimal, circulating decimal, repetend; common measure, aliquot part; prime number, prime, relative prime, prime factor, prime pair; reciprocal; totient.
Source: adapted from Roget's Thesaurus.

Crosswords: Product

English words defined with "product": animal product ♦ cross product ♦ dot product ♦ end product ♦ inner product ♦ mathematical product ♦ plant product, product development, product introduction, product line, product research ♦ Residual product ♦ scalar product ♦ Universal Product Code ♦ vector product. (references)

Specialty definitions using "product": acid refractory product, application specific standard product, ASSEMBLER, PRODUCT, associated product ♦ BH product, BROWSE DATA PRODUCT, bundled air transport product ♦ Cartesian product ♦ dangerous product, DATA PRODUCT LEVEL, daughter product, decay product, direct product, director, product assurance ♦ ESSENTIAL DATA PRODUCT ♦ gross national product at market prices ♦ homeopathic medicinal product ♦ immunological veterinary medicinal product, intermediate catabolic product ♦ Kronecker product of matrices ♦ like product, logical product ♦ Manufacturing Use Product, minimum product firing temperature ♦ outer product ♦ packaged petroleum product, prepackaged product, pre-packaged product, product co-ordinator, product cycle, product data management, Product Labeling, Product Level, product model, Product Packaging, proprietary medicinal product ♦ ready-made veterinary medicinal product ♦ solubility product concentration, source-receiver product, Standard for the exchange of product model data, standardized product, System Product Interpreter ♦ tensor product, tunnel-diode CR product ♦ Virtual Machine/System Product ♦ Water Supply Outlook Product. (references)

Etymologies containing "product": Productus. (references)

Modern Usage: Product

Domain	Usage
Screenplays	I'd say you were using too much of your own product. (Clear and Present Danger; writing credit: Donald Stewart) This is no fantasy - no careless product of wild imagination (Superman; writing credit: Jerry Siegel; Joe Shuster) No Duh. Duh is a product of fear (Donnie Darko; writing credit: Richard Kelly) Bart, tell Dad I will only pass the syrup if it won't be used on any meat product. (The Simpsons; writing credit: Artur Brauner; Paul Hengge) Finally, a product for me (Space Ghost Coast to Coast; writing credit: Ben Karlin)
Lyrics	These ho's don't want him no mo, he's cold product (Lose Yourself; performing artist: EMINEM) Product of my environment, nothing can save me (Anything; performing artist: Jay-Z) Another big news story of year concerned the ecumenical council in Rome, known as Vatican II. Among the things they did in an attempt to make the church more commercial was to introduce the vernacular into portions of the mass, to replace Latin, and to widen somewhat the range of music permissible in the liturgy, but I feel that if they really want to sell the product, in this secular age, what they ought to do is to redo some of the liturgical music in popular song forms (The Vatican Rag; performing artist: Tom Lehrer)
Clever	It is not the employer who pays wages, he only handles the money. It is the product that pays wages. (references; author: unknown)
Movie/TV Titles	A Finished Product (1917) The Mark Thomas Comedy Product (1996)
Source: compiled by the editor from various references; see credits.

Commercial Usage: Product

Domain	Title
References	Pharmaceutical Product Development: International Competitive Benchmarks and Financial Gap Analysis (reference) Muehl Product & Service AG: International Competitive Benchmarks and Financial Gap Analysis (reference) The 2001 Kiribati Economic and Product Market Databook (reference) The 2001 Pacific Islands Trust Economic and Product Market Databook (reference) The 2001 Christmas Island Economic and Product Market Databook (reference) (more reference examples)

Books	Biotechnology for Control of Growth and Product Quality in Swine: Implications and Acceptability (reference) Secret Formula: How Brillant Marketing and Relentless Salesmanship Made Coca-Cola the Best-Known Product in the World (reference) Human Resource Management with West Group Product Booklet (reference) Market Overview: Collaborative Product Development: Giga Planning Assumption [DOWNLOAD: PDF] (reference) Analyses of coal product samples of producing South African collieries (reference) (more book examples)

Periodicals	Buildcore Product Source (reference) Computer Product News (reference) Construction Product Library - Cd Rom (reference) (more periodical examples)

Theater & Movies	Emergency Broadcast Network: Commercial Entertainment Product (reference) Hand Maid May - Product Recall (Vol. 2) (reference) (more DVD examples; more video examples)

Music	Product of Deceit & Loneliness (reference) Product Placement [IMPORT] (reference) Product Deluxe Presents: For Successful [IMPORT] (reference) Not A Viable Commercial Product (reference) Juvenile Product of the Working Class (reference) (more classical music examples; more popular music examples)

High Tech	3dfx Velocity 4MB UPG Daughter Board For Velocity 3D Product Only (reference) Macromedia Studio MX-Mac Upgrade from 2+ Macromedia product (reference) Road Warrior International Multinational To Us Power Adapt Allows Foreign Product Usage In Us (reference) Raptor FW with VPN Server 6.5 Product Kit (100-user) (reference) Client/server/messaging Suite Regular Product 25U (reference) (more camera examples; more video game examples; more computer examples; more electronic examples; more software examples)

Consumer Goods	PRODUCT FIN CORP Luggage Cart (reference) Gardena 36001-12 Product Adaptor (reference) (more baby examples; more wireless phone examples; more garden examples; more kitchen examples; more tool examples)
Source: compiled by the editor from various references; see credits.

Image Slideshow: Product

Photo Album: Product

Thumbnail	Description & Credit	Thumbnail	Description & Credit
	After drugs enter the cell passively they are actively kicked out by the MDR gene product (glycoprotein) which acts as a pump. A drug like verapamil blocks the pump by inhibiting binding of the drug to the pump. Credit: Unknown photographer/artist.		A microgametocyte, a product of the erythrocytic cycle, is shown in an oval RBC. The ingestion of the gametocytes by an Anopheles sp. mosquito begins the parasitic multiplication process during the Sporogonic Cycle. Credit: CDC.
	A macrogametocyte is a product of the erythrocytic life cycle. Both the male and female gametocytes can be ingested by an Anopheles sp. mosquito, whereupon, exflagellation of microgametocytes occurs, and the macrogametocytes are fertilized. Credit: CDC.		The mature schizont of P. vivax contains 12 - 24 merozoites, a product of asexual division. It will eventually rupture, and the merozoites will invade other erythrocytes to repeat the erythrocytic schizogony, or will develop into gametocytes. Credit: CDC.
	Bureau of Commercial Fisheries Ship DAVID STARR JORDAN - the finished product. Credit: Sailing for Science - the NOAA Fleet Then and Now.		Figure 37. Bucknill-Casella manometric sounder, invented by Lieutenant John T. Bucknill of the Royal Engineers of the Royal Navy in 1870 to mitigate problems with existing sounding systems. This sounder was based on Bourdon's tube, whose curvature varied as a function of the pressure difference between the interior and the fluid in which it was immersed. Louis P. Casella made the final product. Credit: Sailing for Science - the NOAA Fleet Then and Now.
	An ARS scientist clanged the way that fermented meats like pepperoni and Genoa salami are made. He found that a bacterial starter stimulates faster, more consistent fermentation than traditional methods and guarantees a better product. P. Credit: USDA ARS News; photo by Scott Bauer..		New uses for cornstarch continue to surprise us. for example, when ARS scientists married starch to a synthetic chemical, they managed to create a product so thirsty, it could absorb hundreds of times its own weight in water. Someone called it SuperSlurper, and the name stuck. P. Credit: USDA ARS News; photo by Scott Bauer..
	Now San Francisco-style sourdough bread can be baked anywhere in the world. Which turned out not to be bad news for the City by the Bay. Pure cultures of L. sanfranciscoare now grown commercially and are commonly used by San Francisco bakers to control the quality of their product. P. Credit: USDA ARS News; photo by Scott Bauer..		Special Forest Product (Bear Grass). Credit: D. Huntington.
Source: pictures compiled by the editor from various references; see picture credits.

Digital Photo Gallery: Product


"This product contains used par" by Feike Kloostra Commentary: "A label on a server titled 'This product contains used parts'."	"Pearl Monument" by Ivan Raszl Commentary: "The Pearl Monument, also known as the GCC monument simbolizes the 6 GCC countries. The huge concrete ball simbolizes a natural pearl, which was Bahrain's most important export product before the oil was found in the region."
Source: photographs selected by the editor, with permission from the photographers.

Familiar Quotations: Product

Author	Quotation
Charles Baudelaire	Everything that is beautiful and noble is the product of reason and calculation.
	Evil is done without effort, naturally, it is the working of fate; good is always the product of an art.
Denis Diderot	It is said that desire is a product of the will, but the converse is in fact true: will is a product of desire.
Johann Friedrich Von Schiller	Measure not by the scale of perfection the meager product of reality.
Judith Plaskow	Human beings are fundamentally communal; our individuality is a product of community, and our choices are shaped by our being with others.
Thomas Carlyle	For man is not the creature and product of Mechanism; but, in a far truer sense, its creator and producer.
Source: compiled by the editor from various references.

Historic Usage: Product

Author	Date	Quotation
John Locke	1690	As much land as a man tills, plants, improves, cultivates, and can use the product of, so much is his property. (Second Treatise of Government)
Communist Manifesto	1848	The other classes decay and finally disappear in the face of Modern Industry; the proletariat is its special and essential product. (reference)
Treaty of Versailles	1919	The amount of each product which may be thus sent annually into Germany shall not exceed the average of the amounts sent annually in the years 1911-1913. (reference)
Miranda v. Arizona	1966	Unless adequate preventive measures are taken to dispel the compulsion inherent in custodial surroundings, no statement obtained from the defendant can truly be the product of his free choice. (reference)
Source: compiled by the editor from various references.

Use in Literature: Product

Title	Author	Quote
Scarlet Letter	Hawthorne, Nathaniel	An imp of evil, emblem and product of sin, she had no right among christened infants
Les Miserables	Hugo, Victor	Which seems the product of the accouchement of Paris
Source: compiled by the editor from various references.

Non-Fiction Usage: Product

Subject	Topic	Quote
Health		Each OTC product contains one of the following active ingredients. (references)
		Ask your doctor if you should use a sunscreen or a sunblocking product. (references)
		The final product contains no more than 2.4 mg of aluminum hydroxide as adjuvant. (references)
Business		They are picky about product flaws. (references)
		Import climate is favorable to the U.S. product. (references)
		Product information in French is vital in Morocco. (references)
Children	Pakistan	Development experts point to a number of factors for the poor state of public education, including the low percentage of gross national product devoted to education and inefficient and corrupt federal and provincial bureaucracies. (references)
Civil Liberties	Philippines	Such remittances amount to nearly 10 percent of the gross national product. (references)
Economic History	Korea	In light of the competition offered by Japanese suppliers, who often visit potential and existing customers throughout Korea, U.S. suppliers should consider (1) making visits to Korea to augment the efforts of the local representative; (2) bringing representatives back to the home office periodically to ensure they are fully informed, motivated and up-to-date on the supplier and its offerings; (3) allowing the distributor or agent to appropriately choose among the U.S. company's full product line selection for sale in the Korean market, (4) holding more demonstrations, seminars and exhibitions of their products in Korea; (5) increasing the distribution of technical data and descriptive brochures; and (6) improving follow-up of initial sales leads. (references)
Minorities	France	Panda claimed that critical statements by government officials in press articles that linked the product to Scientology have caused a significant loss of business. (references)
Political Economy	SPAIN	The U.S.-EU Mutual Recognition Agreement, when fully implemented, will permit certain conformity assessments (e.g., product tests) to be performed in the United States to EU requirements. (references)
	Brazil	By most measures -- geographic size, population, and gross economic product -- Brazil is South America's dominant country. (references)
Political Rights	Zimbabwe	The NCA openly was critical of the CC, asserting that it was a government-controlled entity whose product would not reflect the will of the populace. (references)
Trade	Austria	If replacement parts for warranty or non-warranty repairs of a product are brought into Austria on a temporary base and the products are re-exported after repair, no duties and taxes will be charged for this transaction. (references)
	Argentina	An inspector from SENASA carries out a visual inspection of the merchandise in order to confirm that it is free of quarantine pests or diseases, and then the product is authorized to enter Argentina. (references)
Travel	Guatemala	Small quantities of product samples usually are entered without a problem. (references)
	Spain	While an increasing number of business people speak English, product literature, correspondence and negotiations in Spanish provide a distinct advantage over competitors who use only English. (references)
	Moldova	The quantity of goods should not exceed the number stipulated in the 2001 Budget Law, which is usually no more than several pieces of each product. (references)
Worker Rights	Singapore	Besides these labor dispute mechanisms and the close working relationship and shared views among labor, management, and the Government, the maintenance of labor peace has been a product of high economic growth rates, regular wage increases, and a high degree of job mobility in a virtual full-employment economy. (references)
	Venezuela	Total take-home pay in the private sector, the product of a presidential decree, was at least equal to that received by public sector minimum wage workers. (references)
	Honduras	A monthly increase of $10 (150 lempiras) was retroactive to October 1, 2000, and an additional monthly increase of $13.33 (200 lempiras) took effect on February 1. This agreement excluded workers in the nonexport agricultural sector, who instead received a monthly wage increase of $10 (150 lempiras) as of February 1. Under this agreement, workers earning between $140 (2,100 lempiras) and $400 (6,000 lempiras) per month received an additional wage increase of $23.33 (350 lempiras) as of April 1. This wage increase excluded: workers receiving a salary increase equivalent to, or greater than, $23.33 (350 lempiras) through either an individual contract or a collective bargaining agreement taking effect 3 months prior to April 1; those paid by piecework or based on productivity; microenterprises, agricultural firms, or ranches employing 15 or fewer workers; and workers in medicine or petroleum product sales whose profit margins are regulated by the Government. (references)
Lexicography	Devil's Dictionary	TAIL, n. The part of an animal's spine that has transcended its natural limitations to set up an independent existence in a world of its own. Excepting in its foetal state, Man is without a tail, a privation of which he attests an hereditary and uneasy consciousness by the coat-skirt of the male and the train of the female, and by a marked tendency to ornament that part of his attire where the tail should be, and indubitably once was. This tendency is most observable in the female of the species, in whom the ancestral sense is strong and persistent. The tailed men described by Lord Monboddo are now generally regarded as a product of an imagination unusually susceptible to influences generated in the golden age of our pithecan past.
Source: compiled by the editor from ICON Group International, Inc.; see credits.

Spoken Usage: Product

Speaker	Phrase(s)
Andrew Weil	You get them in many health food stores. There is a product out there called Microsoft that I like, there's another product called Host Defense. Read the labels, go to my web site for more information about it.
Priscilla Presley	Well, he grew up in it. He was a product of the business. And that was his only way of life. He loved it. He, you know, he traveled all over before he was even really discovered by Colonel Parker. And had venues that he would appear at.
Rush Limbaugh	We even make beer companies run a portion of their advertising which is oriented toward convincing people not to by their product, much like we tell the tobacco companies to do.
Source: compiled by the editor from various references; see credits.

Speeches: Product

Speaker	Term	Phrase(s)
John Adams	1797-1801	I observe with much satisfaction that the product of the revenue during the present year has been more considerable than during any former equal period.
James Madison	1809-1817	To a thriving agriculture and the improvements related to it is added a highly interesting extension of useful manufactures, the combined product of professional occupations and of household industry.
Benjamin Harrison	1889-1893	The cotton plantation will not be less valuable when the product is spun in the country town by operatives whose necessities call for diversified crops and create a home demand for garden and agricultural products.
Lyndon B. Johnson	1963-1969	We enacted the Wholesome Meat Act, the Flammable Fabrics Act, the Product Safety Commission, and a law to improve clinical laboratories.
Jimmy Carter	1977-1981	This will necessitate adoption of a broader concept of health care, to include such areas as environmental health, workplace health and safety, commercial product safety, traffic safety, and health education, promotion and information.
Ronald Reagan	1981-1989	Our current problems are not the product of the recovery program that is only just now getting under way, as some would have you believe.
George Bush	1989-1993	When health coverage for a fellow on the assembly line costs thousands of dollars, the cost goes into the product he makes.
Source: compiled by the editor from various references.

Usage Frequency: Product

"Product" is generally used as a noun (singular) -- approximately 99.98% of the time. "Product" is used about 11,101 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted)

Parts of Speech	Percent	Usage per 100 Million Words	Rank in English
Noun (singular)	99.98%	11,099	836
Total	100.00%	11,101	N/A

Source: compiled by the editor from several corpora; see credits.

Usage in Company Names: Product

Country	Name	Country	Name
Germany	Muehl Product & Service AG	USA	Pharmaceutical Product Development
	(more examples...)

Source: compiled by the editor from Icon Group International, Inc.

Expressions: Product

Expressions using "product": acceptable product ♦ adulterated product ♦ agricultural product ♦ animal product ♦ application specific standard product ♦ associated product ♦ best product ♦ BH product ♦ branded product ♦ bulk petroleum product ♦ bundled air transport product ♦ by product ♦ cartesian product ♦ cleaning product ♦ Condensation product ♦ cosmetic product ♦ cross product ♦ dairy product ♦ dangerous product ♦ daughter product ♦ decay product ♦ direct product costs ♦ domestic product ♦ dot product ♦ end product ♦ excretory product ♦ fishery product ♦ fission product ♦ food product ♦ genetically modified product ♦ GM product ♦ gross domestic product &dia