counterexample

[Waisher]

refutation by example

[Laresvog 0]

A counterexample is a specific instance or example that contradicts a general claim, principle, theorem, or proposition, proving it to be false or incorrect. It is often used as a method of disproving statements or theories in logic, mathematics, and various fields of study.

[DebrahCom]

In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule. For example, consider the proposition all students are lazy. Because this statement makes the claim that a certain property holds for all students, even a single example of a diligent student will prove it false. Thus, any hard-working student is a counterexample to all students are lazy. More precisely, a counterexample is a specific instance of the falsity of a universal quantification.
In mathematics, this term is also sometimes used for examples illustrating the necessity of the full hypothesis of a theorem, by considering a case where a part of the hypothesis is not verified, and where one can show that the conclusion does not hold. A counterexample may be local or global in an argument.

[MonicaLes]

An exception to a proposed general rule; a specific instance of the falsity of a universally quantified statement.