Domain
- Category
- STANDARD MATHEMATICS
- Definition
- The set of inputs for which a function, equation or mathematical object is being considered.
- Math Level
- GENERAL
The domain of a function or statement is the set of inputs or cases to which it applies.
Domain matters because “always” only has meaning relative to an allowed set. A counterexample must lie inside the claimed domain, and a positivity result must specify where the quantity is required to stay non-negative.
See also: universal statement, counterexample, pointwise property, global property..