Full Idea
Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument.
Gist of Idea
Later Frege held that definitions must fix a function's value for every possible argument
Source
report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv
Book Reference
Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.109
A Reaction
Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'.