Definition:Real Function/Definition 1
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Definition
Let $S \subseteq \R$ be a subset of the set of real numbers $\R$.
Suppose that, for each value of the independent variable $x$ of $S$, there exists a corresponding value of the dependent variable $y$.
Then the dependent variable $y$ is a (real) function of the independent variable $x$.
Also see
- Results about real functions can be found here.
Sources
- 1914: G.W. Caunt: Introduction to Infinitesimal Calculus ... (previous) ... (next): Chapter $\text I$: Functions and their Graphs: $2$. Functions
- 1963: Morris Tenenbaum and Harry Pollard: Ordinary Differential Equations ... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $2 \text B$: The Meaning of the Term Function of One Independent Variable: Definition $2.3$
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $8$: The System of the World: Calculus