mittenäited

Mittenäited (from Estonian mitte 'not' and näide 'example') refers to an example that does not satisfy a given statement or hypothesis. In logic and mathematics, a mittenäide demonstrates that a general claim is not true in all cases, i.e., it is a counterexample. A single mittenäide is enough to refute a universal statement and helps identify the conditions under which a claim holds.

In practice, mittenäited are used to test hypotheses, to illustrate the limits of theorems, or to clarify definitions. For instance, the statement "all natural numbers are even" is incorrect, and the mittenäide 1 shows its falsity. More constructively, a mittenäide often reveals why a theorem's proof requires certain assumptions or why a condition is necessary.

Outside formal mathematics, mittenäited appear in language studies and pedagogy as a tool for teaching critical thinking and precision. They show that rules may have exceptions or specific domains of applicability, and they aid in distinguishing between universal claims and statements that hold only under certain restrictions.