Definition:Preimage of Element under Mapping/Also known as

Preimage of Element under Mapping: Also known as

The preimage of an element is also known as its inverse image.

In other contexts, this is called the fiber of $t$ (under $f$).

The UK English spelling of fiber is fibre.

The term argument is popular in certain branches of mathematics.

If $\tuple {x, y} \in f$, then $x$ is the argument (of $f$) which holds the value $y$.

In the context of computability theory, the following terms are frequently found:

If $\tuple {x, y} \in f$, then $x$ is often called the input of $f$ which produces the output $y$.

Sources

• 1951: Nathan Jacobson: Lectures in Abstract Algebra: Volume $\text { I }$: Basic Concepts ... (previous) ... (next): Introduction $\S 3$: Equivalence relations
• 1959: E.M. Patterson: Topology (2nd ed.) ... (previous) ... (next): Chapter $\text {II}$: Topological Spaces: $\S 9$. Functions
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): argument (of a function)

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• 1964: William K. Smith: Limits and Continuity ... (previous) ... (next): $\S 2.2$: Functions: Exercise $\text{A} \ 5 \ \text{(b)}$
• 1965: Claude Berge and A. Ghouila-Houri: Programming, Games and Transportation Networks ... (previous) ... (next): $1$. Preliminary ideas; sets, vector spaces: $1.1$. Sets
• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 0.4$
• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Functions
• 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $\S 1.3$: Functions and mappings. Images and preimages
• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 2$: Sets and functions: Graphs and functions
• 1989: George S. Boolos and Richard C. Jeffrey: Computability and Logic (3rd ed.) ... (previous) ... (next): $1$ Enumerability
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): argument: 1.
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): Appendix $\text{A}.3$: Functions
• 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): Appendix $\text{A}$: Set Theory: Functions
• 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions