volume_mute
A Function That Has No Formula
publish date: 2026/05/23 18:30:38.913982 UTC
volume_mute
Which of the following is an example of a function defined by a statement rather than an algebraic formula?
Correct Answer
The n-th digit in the decimal expansion of \(\pi\)
Explanation
The rule of association for a function need not be an algebraic formula — it can be any unambiguous statement. "The \(n\)-th digit in the decimal expansion of \(\pi\)" perfectly defines a function of \(n\) (domain = natural numbers), yet no closed algebraic formula for it exists. This illustrates that formulas and functions are not the same concept.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012