Counterexamples: Disproving General Statements in Mathematics

counterexample

A counterexample is a specific example or scenario that disproves a statement or claim

A counterexample is a specific example or scenario that disproves a statement or claim. It is used to show that a general statement does not always hold true.

For example, let’s consider the claim that “all prime numbers are odd.” To provide a counterexample, we need to find a prime number that is not odd.

The number 2 is a prime number but it is the only even prime number. Therefore, the claim that all prime numbers are odd is disproven by the counterexample of 2.

This counterexample shows that there is at least one prime number that is not odd, which contradicts the initial claim.

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