Counterexample
A counterexample is an example that disproves a statement or claim
A counterexample is an example that disproves a statement or claim. In mathematics, it is used to show that a general statement is not always true by providing a specific case where it fails to hold. By finding a single counterexample, we can conclude that the statement is false.
For instance, let’s consider the statement “All prime numbers are odd.” To disprove this statement, we need to find a prime number that is not odd.
One counterexample to this statement is the number 2. In contrast to other prime numbers, 2 is the only even prime number. Therefore, the statement “All prime numbers are odd” is false, since we have found a counterexample (2) that contradicts it.
In mathematics, counterexamples play a crucial role in disproving conjectures, demonstrating the necessity of certain conditions, or showing that a general claim does not hold in every case. They help us refine our understanding of mathematical concepts by identifying exceptions to statements or the limitations of certain theorems.
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