Triviality (mathematics)

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or a particularly simple object possessing a given structure (e.g., <a href="/facts/Group_(mathematics)/IQTYqINt">group</a>, <a href="/facts/Topological_space/v2ut7CbK">topological space</a>). The noun triviality usually refers to a simple technical aspect of some proof or definition. The origin of the term in mathematical language comes from the medieval <a href="/facts/Trivium_(education)/F180PttJ">trivium</a> curriculum, which distinguishes from the more difficult <a href="/facts/Quadrivium/Qm48ab6G">quadrivium</a> curriculum. The opposite of trivial is nontrivial, which is commonly used to indicate that an example or a solution is not simple, or that a statement or a theorem is not easy to prove.
</p><p>Triviality does not have a rigorous definition in mathematics. It is <a href="/facts/Subjectivity_and_objectivity_(philosophy)/YhXxVe8g">subjective</a>, and often determined in a given situation by the knowledge and experience of those considering the case.
</p>

Triviality (mathematics) open-in-new

Triviality (mathematics)