Argument
Range of a function
Overview
In mathematics, the range of a function may refer either to the codomain of the function, or the image of the function.
In some cases the codomain and the image of a function are the same set; such a function is called surjective or onto. For any non-surjective function
f
:
X
→
Y
,
{\displaystyle f:X\to Y,}
the codomain
Y
{\displaystyle Y}
and the image
Y
~
{\displaystyle {\tilde {Y}}}
are different; however, a new function can be defined with the original function's image as its codomain,
f
~
:
X
→
Y
~
{\displaystyle {\tilde {f}}:X\to {\tilde {Y}}}
where
f
~
(
x
)
=
f
(
x
)
.
{\displaystyle {\tilde {f}}(x)=f(x).}
This new function is surjective.
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.
Nevertheless, it has some serious defects. In the first place, it turns upon metrical considerations; while the distinction between a continuous and a discontinuous series is manifestly non-metrical. In the next place, a perfect series is defined as one containing “every point” of a certain description. But no positive idea is conveyed of what all the points are: that is definition by negation, and cannot be…
Charles S. Peirce, Chance, Love, and Logic
States what Range of a function is.
(2) _Non-inductiveness._--The second property by which infinite numbers are distinguished from finite numbers is the property of non-inductiveness. This will be best explained by defining the positive property of inductiveness which characterises the finite numbers, and which is named after the method of proof known as "mathematical induction." Let us first consider what is meant by calling a property "hereditary"…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
States what Range of a function is.
Thus there arises a classification of modes of formation, or in the language commonly used by mathematicians, a classification of Functions. Any number, considered as formed from any other number, is called a function of it; and there are as many kinds of functions as there are modes of formation. The simple functions are by no means numerous, most functions being formed by the combination of several of the…
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
States what Range of a function is.
Related ideas
Place in the tradition
Part of Outline of logic.