Counterexample
In mathematics, a counterexample is an example that disproves a statement or a conjecture
In mathematics, a counterexample is an example that disproves a statement or a conjecture. It is a specific instance or case that contradicts a proposed general rule or theory. By providing a counterexample, we show that the statement is not universally true and that it fails in at least one circumstance.
To illustrate this concept, let’s consider the following conjecture:
“All odd numbers are prime.”
To verify if this statement is true, we need to check if every odd number is indeed prime. However, we can provide a counterexample that disproves this conjecture. For instance, the number 9 is an odd number, but it is not prime since it can be divided by 3.
By demonstrating that the statement fails and presenting a specific example where it does not hold, we provide a counterexample. Counterexamples play a crucial role in mathematics since they help refine and improve conjectures, theories, and definitions, leading to a better understanding of mathematical concepts.
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