Niettriviale

Niettriviale is a Dutch adjective meaning not trivial. It is used to describe objects, results, or arguments that have substantive content beyond what is immediately obvious or degenerate. The term is common in mathematical and logical discourse, but also appears in general discussions to indicate significance or depth.

Etymology and usage patterns: the word is formed from niet (not) and triviaal (trivial). In contemporary Dutch, niettriviale is typically used attributively before a noun, for example niettriviale oplossin­gen (nontrivial solutions), niettriviale eigenschap (nontrivial property), or niettriviale topologie (nontrivial topology). Some older or stylistic texts may hyphenate as niet-triviaal, but niettriviale is widely accepted in modern usage.

Mathematical context: nontrivial is the standard English counterpart, and niettriviale is employed to distinguish cases with meaningful structure from trivial or degenerate ones. Examples include nontrivial solutions to equations (solutions other than the obvious or zero solution), nontrivial subgroups of a group, nontrivial kernels of linear maps, or topological spaces with features not homotopy-equivalent to a single point. The label signals that the object cannot be reduced to a simpler, empty, or universally obvious case.

Other domains: outside mathematics, niettriviale describes arguments, proofs, or claims that provide substantial content rather than tautologies or vacuous statements. It is often used to emphasize depth, difficulty, or relevance in philosophical or theoretical contexts.

See also: trivial, nontrivial, nontrivial solution.