Definition:Image of Element under Mapping/Also known as
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Definition
The image of an element $s$ under a mapping $f$ is also called the functional value, or value, of $f$ at $s$.
The terminology:
- $f$ maps $s$ to $\map f s$
- $f$ assigns the value $\map f s$ to $s$
- $f$ carries $s$ into $\map f s$
can be found.
The modifier by $f$ can also be used for under $f$.
Thus, for example, the image of $s$ by $f$ means the same as the image of $s$ under $f$.
In the context of computability theory, the following terms are frequently found:
If $\tuple {x, y} \in f$, then $y$ is often called the output of $f$ for input $x$, or simply, the output of $f$ at $x$.
Sources
- 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Functions
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 2$: Sets and functions: Graphs and functions
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 4$. Relations; functional relations; mappings: Remark $1$
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 20$: Introduction: Remarks $\text{(g)}$