Wikipedia 10K Redux

Reconstructed by Reagle from Starling archive; see blog post for context.

Function

In Mathematics, a means of associating two (or more) quantities (or variables). Each variable has a disinctive role.

*Roles of the variables

  • The independent variable is a value selected from a set called the domain of the function.
  • The dependent variable is a value (in a set called the range of the function) which is determined by the value of the independent variable.

    • *Specification of the function

  • A function may be specified by giving an algorithm (or rule) which yields the value of the dependent variable when the value of the independent variable is provided as input.
  • A function may be specified by a of ordered pairs of values.
  • A function may be described by a graph of points in two dimensions presenting (conventionally) the independent variable as the horizontal component and the dependent variable as the vertical component.

    • *Related concepts

    :The concept of a function has been generalized to include arbitrary domains and ranges, the most common on which is the vector valued function in which the range is a set, not of numbers, but of n-tuples or vectors.

    :We sometimes distinguish between function definitions which are given by intention, that is by an algorithm and those given by extension, those specified by a list of pairs.

    :Continuous Functions are those whose domains and ranges are sets of real numbers and which satisfy additional constraints.

    Also called a Mapping.

    Dick Beldin