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Best Mode When the Domain is an Infinite Set
publish date: 2026/05/23 18:30:36.041575 UTC
volume_mute
When the domain of a function is an infinite set, which mode of expressing the function is considered the most accurate and complete?
Correct Answer
Statement of the rule of association (by formula or otherwise)
Explanation
For an infinite domain, a formula or rule of association is the only truly accurate mode. Tables are limited to small, finite domains. Listing ordered pairs is impossible for infinite sets. Graphs are useful but require a formula for the function to be fully defined. An interesting special case: the \(n\)-th digit of \(\pi\) is a valid function defined by a statement, not a formula.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012