Argument
Domain of a function
Overview
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by
dom
(
f
)
{\displaystyle \operatorname {dom} (f)}
or
dom
f
{\displaystyle \operatorname {dom} f}
, where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be".
More precisely, given a function
f
:
X
→
Y
{\displaystyle f\colon X\to Y}
, the domain of f is X. In modern mathematical language, the domain is part of the definition of a function rather than a property of it.
In the special case that X and Y are both sets of real numbers, the function f can be graphed in the Cartesian coordinate system. In this case, the domain is represented on the x-axis of the graph, as the projection of the graph of the function onto the x-axis.
For a function
f
:
X
→
Y
{\displaystyle f\colon X\to Y}
, the set Y is called the codomain: the set to which all outputs must belong. The set of specific outputs the function assigns to elements of X is called its range or image. The image of
f
{\displaystyle f}
is a subset of Y, shown as the yellow oval in the accompanying diagram.
Any function can be restricted to a subset of its domain. The restriction of
f
:
X
→
Y
{\displaystyle f\colon X\to Y}
to
A
{\displaystyle A}
, where
A
⊆
X
{\displaystyle A\subseteq X}
, is written as
f
|
A
:
A
→
Y
{\displaystyle \left.f\right|_{A}\colon A\to Y}
.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
And since this harmony of the object with the faculties of the subject is contingent, it brings about the representation of its purposiveness in respect of the cognitive faculties of the subject.
Immanuel Kant, Kant's Critique of Judgement
States what Domain of a function is.
We can arbitrarily exclude any set of events at the big end of an abstractive set without the loss of any important property to the set as thus modified. I call the limiting character of natural relations which is indicated by an abstractive set, the 'intrinsic character' of the set; also the properties, connected with the relation of whole and part as concerning its members, by which an abstractive set is defined…
Alfred North Whitehead, The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919
States what Domain of a function is.
We thus obtain, on the straight line in question, a continuous series of points, which, since it is continuous, we regard as constituting our straight line. It is thus solely from the hypostatizing of relations, which metrical Geometry requires, that the view of straight lines and planes as _composed_ of points arises, and it is from this hypostatizing that the difficulties of metrical Geometry spring. =132.= The…
Bertrand Russell, An essay on the foundations of geometry
States what Domain of a function is.
Related ideas
- Integer
- Function (mathematics)
- Mathematics
- Real number
- Set (mathematics)
- Set theory
- Topological space
- Mathematical analysis
- Empty set
- Range of a function
Place in the tradition
Part of Outline of logic.