Single-valued Function (Noun)
Meaning
(mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function).
Classification
Nouns denoting relations between people or things or ideas.
Examples
- A function is said to be single-valued if each input in the domain maps to exactly one output in the range, making it a well-defined relation.
- In single-valued functions, every input has a unique corresponding output, eliminating any ambiguity in the mapping.
- To evaluate a function as single-valued, one must determine whether every element in the domain corresponds to a unique element in the range.
- Single-valued functions exhibit distinct behavior that separates them from multivalued functions, where a single input can produce multiple outputs.
- When defining a new function, mathematicians verify that it qualifies as single-valued by checking that each domain element can be paired with at most one corresponding range element.