counterexample. A counterexample is an example that contradicts or disproves a statement or claim. In the context of definition, if a statement fails to encompass all the necessary conditions or includes irrelevant or incorrect elements, it can be considered a poor or incomplete definition. By providing a counterexample, we can demonstrate that the statement does not hold true in all cases and therefore does not meet the criteria for a good definition. Additionally, a counterexample helps to illustrate the limitations or gaps in the statement, highlighting the need for revision or clarification.
counterexample. A counterexample is an example or situation that contradicts the statement being defined. By providing a counterexample, we can demonstrate that the statement does not hold true in all cases, therefore suggesting that it is not a good definition.
