nichttrivialen

Nichttrivialen is a German adjective meaning not trivial. It is used to describe problems, solutions, proofs, models, or other objects that are not obvious, not reducible to a simple case, or that require non-obvious reasoning. The term is common in mathematics, logic, philosophy, and computer science, where it signals that a result or item has substantive content beyond the obvious or degenerate case.

Etymology and sense: the word combines nicht- with trivial, the latter rooted in Latin trivialis. In everyday usage the sense of nichttrivial is to emphasize significance, complexity, or structure that cannot be deduced from a straightforward or routine consideration.

Usage and examples: in mathematical and logical contexts, one speaks of nichttriviale Lösungen, nichttriviale Beweise, and nichttriviale Modelle to indicate nontrivial solutions, proofs, or models. For instance, a nichttriviale Lösung would be a solution that is not immediately obvious or not merely a special case of a general method. In philosophy or computer science, nontrivial arguments or nontriviale Algorithmen may be described similarly.

Inflection and form: in German, the ending of nichttrivial- adjectives changes with gender, number, and case. The form nichttrivialen is an inflected variant used in certain phrases, such as after a definite article in plural (die nichttrivialen Beweise). Other endings occur in different grammatical contexts, yielding nichttriviale or other forms.

See also: Trivialität and Nichttrivialität, terms that describe the opposite concepts or related ideas of simplicity versus non-obviousness.