**R. A. Schwaller de Lubicz**

"

*If, on the other hand, we see an image that represents a man walking (or simply lines depicting a man) we no longer imagine him, we no longer situate him; he is there, it is the*" [R. A. Schwaller de Lubicz, The Temple in Man, page 18]

**function**that interests us, and the quality of that**function**. We can then paint this man green: it will no longer be solely the**function**of walking with one's legs that is evoked - this movement could also signify vegetation or growth. But to our reason, walking and growing are two different**functions**, while in reality there is an abstract connection between them: it is movement outside consideration of Time, or pathway, or specific direction."Proportion belongs to geometry and harmony, measurement to the object and to arithmetic; and one necessitates the other. Proportion is the comparison of sizes; harmony is the relationship to measures; geometry is the

**function**of numbers." [R. A. Schwaller de Lubicz, The Temple in Man, page 61]

**Orthodox**

A

**function**, in mathematics, associates one quantity, the argument of the

**function**, also known as the input, with another quantity, the value of the

**function**, also known as the output. A

**function**assigns exactly one output to each input. The argument and the value may be real numbers, but they can also be elements from any given set. An example of a

**function**is f(x) = 2x, a

**function**which associates with every number the number twice as large. Thus 5 is associated with 10, and this is written f(5) = 10.

The input to a

**function**need not be a number, it can be any well defined object. For example, a

**function**might associate the letter A with the number 1, the letter B with the number 2, and so on. There are many ways to describe or represent a

**function**, such as a formula or algorithm that computes the output for a given input, a graph that gives a picture of the

**function**, or a table of values that gives the output for certain specified inputs. Tables of values are especially common in statistics, science, and engineering.

The set of all inputs to a particular

**function**is called the domain. In modern mathematics functions are normally defined to have a codomain associated with them which is some fixed set which includes all possible outputs, for instance real valued functions have a codomain which includes all the real numbers even though each particular real valued

**function**may not include every real number as an output. The set of all the ordered pairs or inputs and outputs (x, f(x)) of a

**function**is called its graph. A common way to define a

**function**is as the triple (domain, codomain, graph), that is as the input set, the possible outputs and the mapping for each input to its output.

The set of all outputs of a particular

**function**is called its image. The word range is used in some texts to refer to the image and in others to the codomain, in particular in computing it often refers to the codomain. The domain and codomain are often "understood". Thus for the example given above, f(x) = 2x, the domain and codomain were not stated explicitly. They might both be the set of all real numbers, but they might also be the set of integers. If the domain is the set of integers, then image consists of just the even integers.

There are many ways to describe or represent

**functions**: for instance by a formula, by an algorithm that computes it, or simply by enumerating its values for every possible argument. A

**function**may also be described through its relationship to other

**functions**, for example, as the inverse function of a given

**function**, or as a solution of a differential equation.

**Functions**can be added, multiplied, or combined in other ways to produce new

**functions**. An important operation on

**functions**, which distinguishes them from numbers, is the composition of

**functions**. There are uncountably many different

**functions**, most of which cannot be expressed with a formula or an algorithm.

Collections of

**functions**with certain properties, such as continuous

**functions**and differentiable

**functions**, are called

**function**spaces and are studied as objects in their own right, in such mathematical disciplines as real analysis and complex analysis. [Source unknown]

See Also

**Calculus**

**Continuity**

**Direction**

**Dynamic**

**fundamental theorem of calculus**

**Laplacian**

**Limit of a Function**

**Neter**

**Potential**

**Principle**

**Scalar**

**Stokes Theorem**

**Symbol**

**Vector**