nichttrivialer

Nichttrivialer is the attributive form of the German adjective nichttrivial, meaning nontrivial or not obvious. The term combines nicht, meaning not, with trivial, which in German and mathematical usage refers to something simple, ordinary, or degenerate. Nichttrivial is used to emphasize that a case, object, or result is more than a straightforward or obvious instance.

In mathematical writing, nichttrivial describes objects that are not the simplest or zero/identity case. Examples include a nichttriviale Lösung (a nontrivial solution) of an equation, a nichttriviale Gruppe (a nontrivial group), or a nichttriviales Beispiel (a nontrivial example). The concept is relative to a chosen baseline of triviality: for instance, the trivial solution to a homogeneous system Ax = 0 is x = 0, and any nonzero vector provides a nichttriviale Lösung. Similarly, a nontrivial kernel or nontrivial homology class signals structure beyond the most basic level.

Outside mathematics, nichttrivial can describe arguments, problems, or phenomena that require substantive reasoning or are not reducible to simple cases. In philosophy, computer science, or physics, the term conveys that the feature in question demands non-obvious analysis or has meaningful complexity.

Declension and usage notes: nach dem unbestimmten Artikel lautet die Form für maskuline Nomen ein nichttrivialer Beweis; feminin eine nichttriviale Lösung; neutrum ein nichttriviales Problem; im Plural nichttriviale Lösungen. The term remains a relative descriptor and should be chosen to reflect context-specific non-obviousness or non-degeneracy.